The Guide, The Way.
Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ is Al Haadi (in Arabic: ٱلْهَادِي), The One who gives guidance to His believers. His Guidance is beneficial and protects them from whatever may be harmful. He is The One who sent prophets (may peace be upon them) as the deliverers of His message to ensure mankind is guided on the right path.
From the root ha-dal-ya (ه د ي), which has the following classical Arabic connotations: to guide rightly, to show with kindness the proper path, to guide on the right path until reaching the goal, to guide aright, to lead the right way.
The Qur'an and The Prophets
This is similar to the Arabic word, Hidayah meaning "guidance." It is also closely related in meaning to the previous name Al-Nur as they both refer to making the path visible, showing the way. Guidance is sent through two means. The primary source for guidance is the literal word of Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ, and that is the Qur'an. The second form of guidance was given through His Prophets and the last Messenger, Prophet Muhammad ﷺ. We study and learn from the Prophetic traditions (what he said and consistently did or encouraged). This is captured through his companions and is mentioned in the hadith book collections. Most notably, Sahih Bukhari, Sahih Muslim, Sunan at-Tirmidhi, Sunan-Ibn Majah, Sunan Abu-Dawud, Sunan Nasa'i. More precedence is given to the first two books, denoted by the title Sahih, meaning authentic. There is a sect among Muslims who refute the guidance provided in the hadith even though the hadith shows us the rites or hajj, wudu, and daily prayer. The Qur'an also addresses this exact issue.
Laqad kaana lakum fee Rasoolil laahi uswatun hasanatul liman kaana yarjul laaha wal yawmal Aakhira wa zakaral laaha kaseeraa
"There has certainly been for you in the Messenger of Allah an excellent pattern for anyone whose hope is in Allah and the Last Day and [who] remembers Allah often." — (Qur'an 33:21)
Qul yaaa aiyuhan naasu innee Rasoolul laahi ilaikum jamee’anil lazee lahoo mulkus samaawaati wal ardi laaa ilaaha illaa Huwa yuhyee wa yumeetu fa aaminoo billaahi wa Rasoolihin Nabiyyil ummiy yil lazee yu’minu billaahi wa Kalimaatihee wattabi’oohu la’allakum tahtadoon
"Say, [O Muhammad], “O mankind, indeed I am the Messenger of Allah to you all, [from Him] to whom belongs the dominion of the heavens and the earth. There is no deity except Him; He gives life and causes death.” So believe in Allah and His Messenger, the unlettered prophet, who believes in Allah and His words, and follow him that you may be guided." — (Qur'an 7:158)
The Guidance of Muhammad (ﷺ) Questioned?
Innaka laa tahdee man ahbabta wa laakinn Allaha yahdee mai yashaaa’; wa huwa a’lamu bil muhtadeen
"Indeed, [O Muhammad], you do not guide whom you like, but Allah guides whom He wills. And He is most knowing of the [rightly] guided." — (Qur'an 28:56)
It is believed, according to Bukhari and Muslim, that this verse was sent to the Prophet ﷺ when his beloved uncle Abu Talib passed away without having converted. From the Tafseer of Abul Ala Maududi, it mentions how the non-believers took this as an opportunity to mock and discredit Prophet Muhammad (ﷺ), saying, "...you wish that your clansmen and your kinsfolk; and your near and dear ones should benefit from this life-giving nectar."
The response Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ gives to Prophet Muhammad (ﷺ) is that he is only but a mere guide. He can show the way to the path, but he can't compel someone to walk it. The only force that has that power is Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ, for He is Al-Hadi. Maududi concludes with the following remark for this ayah, "He wills not on account of a family or tribal relationship, but on the basis of one's sincerity, capability and inclination of the heart." This is why when we make du'a, we ask Allah to increase our imaan (faith) and to make us among those who have the courage, intellect, and strength so that we can walk the straight path.
The second interpretation of what it means for Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ to be referred to as Al-Hadi is expanded with the understanding of this ayah.
Qaala Rabbunal lazeee a’taa kulla shai’in khalqahoo summa hadaa
"He said, 'Our Lord is He who gave each thing its form and then guided [it].'" — (Qur'an 20:50)
From this ayah, we can infer that Allah's guidance is not just an attribute of showing people the path of faith. It is more encompassing than that. Each creation has been divinely guided to what is required to satisfy its needs.
Imam al-Ghazali writes of how an infant knows how to crawl up to the mother's breast and take milk without any intervention (a phenomenon known as "the breast crawl"). It's also why bees build their hives in a hexagonal pattern. It's the most efficient use of space. This shape is better than all others as it requires the least amount of wax to build, creates a compact structure, and leaves the most space for honey and rearing larvae. Everything has been perfectly guided and accounted for.
Wallazee qaddara fahadaa
"And who destined and [then] guided" — (Qur'an 87:3)
We ask to become among those rightly guided. We realize in all our actions, there is an underlying motive, and that reason is to serve Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ. It is an expression of love and servitude. The reason why we pray five times per day, dietary "restrictions," wearing the hijab, and keeping the beard. All of this is for Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ. We should keep this in mind and not forget the purpose of our actions. Don't just fall in love with the routine without thinking of the reason why. Avoid the mindset of doing things just for the sake of doing them. There's a deeper motive to it, and if it's understood, it will make the action sweeter. Remember, in all good that you do, it's to please Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ, to draw closer and strengthen our connection to Him. By realizing this, we may even begin asking upon doing something good if there was a manner in which the act could've been performed that would've been even more pleasing to Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ. This spurs curiosity and motivation to study the Prophetic traditions of Prophet Muhammad ﷺ in all matters. In doing so, you become even more guided.
To characterize oneself by the name Al-Hadi, we ask whether we are good representatives or guides to encourage people to do what's better. The key is to facilitate, which means to make something easier. It does not mean demanding, scolding, judging, being negative, or making others feel miserable. We can even see how the message of Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ is explained in the Qur'an:
Inna haazal Quraana yahdee lillatee hiya aqwamu wa yubashshirul mu’mineenal lazeena ya’maloonas saalihaati anna lahum ajran kabeeraa
"Indeed, this Qur’an guides to that which is most suitable and gives good tidings to the believers who do righteous deeds that they will have a great reward." — (Qur'an 17:9)
It mentions that the Qur'an has been sent to protect noble/upright character. By following this guidance, by doing what is right, you will have a great reward. Like a doctor who warns a diabetic, you can eat sugary foods but be ready to pay the price for not changing your diet. The role taken is an advisory role, not to be Allah's enforcement officer. Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ reveals to Prophet Muhammad ﷺ, "Say [Prophet], ‘People, I am sent only to give you clear warning.’ And those who have believed and done righteous deeds – for them is forgiveness and noble provision. But the ones who strove against Our verses, [seeking] to cause failure – those are the companions of Hellfire." (Qur'an 22:49-51) and also in Surah Hud, "But you are only a warner. And Allah is Disposer of all things." (Qur'an 11:12) So, we should try our best to raise the standard and uplift each other. To encourage good acts, educate, show, explain, and make something as easy as possible to follow.
Narrated Uthman bin Affan: The Prophet ﷺ said, "The most superior among you (Muslims) are those who learn the Qur'an and teach it." 
Narrated Abdullah: Allah's Messenger ﷺ said, "Do not wish to be like anybody except in two cases: The case of a man whom Allah has given wealth and he spends it in the right way, and that of a man whom Allah has given religious wisdom (i.e., Qur'an and Sunna) and he gives his verdicts according to it and teaches it." (to others i.e., religious knowledge of Qur'an and Sunna (Prophet's Traditions)." 
We can learn this du'a which the Prophet Muhammad ﷺ made asking Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ to make us noble, beautify us in faith, and be among those who are rightly guided. Ata bn As-Sa'ib narrated that his father said: "Ammar bin Yasir led us in prayer and he made it brief. Some of the people said to him: 'You made the prayer sort (or brief).' He said: 'Nevertheless I still recited supplications that I heard from the Messenger of Allah (ﷺ).' When he got up and left, a man -- he was my father but he did not name himself -- followed him and asked him about that supplication, then he came and told the people: 
Allahumma bi ilmikal-ghaiba wa qudratika alal-khalqi ahyini ma 'alimtal-hayata khairan li, wa tawaffani idha 'alimtal-wafata khairan li. Allahumma wa as'aluka khashyataka fil-ghaibi wash-shahadati wa as'aluka kalimatal-haqqi fir-rida'i wal ghadab, wa as'alukal-qaṣda fil faqri wal-ghina, wa as'aluka na'iman la yanfadu wa as'aluka qurrata ainin la tanqaṭi'u wa as'alukar-rida'i ba'dal-qada'i wa as'aluka bardal 'aishi ba'dal-mawti, wa as'aluka ladhdhatan-nazari ila wajhika wash-shawqa ila liqa'ika fi ghairi darra'a mudirratin wa la fitnatin mudillatin, Allahumma zayyinna bizinatil-imani waj'alna hudatan muhtadin
"O Allah, by Your knowledge of the unseen and Your power over creation, keep me alive so long as You know that living is good for me and cause me to die when You know that death is better for me. O Allah, cause me to fear You in secret and in public. I ask You to make me true in speech in times of pleasure and of anger. I ask You to make me moderate in times of wealth and poverty. And I ask You for everlasting delight and joy that will never cease. I ask You to make me pleased with that which You have decreed and for an easy life after death. I askYou for the sweetness of looking upon Your face and a longing to meet You in a manner that does not entail a calamity that will bring about harm or a trial that will cause deviation. O Allah, beautify us with the adornment of faith and make us among those who guide and are rightly guided."