The Eternal, Ever-Present, The Immutable.
Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ is Al-Baqi (in Araic: ٱلْبَاقِي), the everlasting. The one who has always existed and who will never cease to be. He is the one whose existence doesn’t have a beginning nor an end. The virtue of this name signifies Allah as being perpetual, endless, and everlasting. He will remain forever and unaffected by time.
From the ba-qaf-ya (ب ق ي) which has the following classical Arabic connotations: To continue, to remain, and to endure. To be permanent, everlasting and constant. To survive forever, to be eternal. To be incessant, continous, and endless.
As we've mentioned in the last name, different scholars have different criteria for what qualifies as a name of Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ. Of the 99 names, 81 are explicitly mentioned in the Qur'an. Therefore, there is not one agreed-upon list for the remaining 18 names. al-Baqi is one of those names which is not included by certain scholars. This list includes Ibn Uthaymeen, Ibn Hazm, and Ibn Hajar, among others. However, others, such as Ibn Arabi, Imam al-Bayhaqi, and al-Ghazali, have included this name in their lists.
We've briefly described this attribute of Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ in al-Awwal (The First) and al-Akhir (The Last), but there is a difference in the interpreted meaning each name conveys. Al-Awwal teaches us about Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ as being the beginning of all creation, al-Akhir describes Him as being the last. However, with al-Baqi, it describes Allah's nature to be everlasting or eternal. Being called the first and the last can seem to be bounded or constrained by time. Al-Baqi affirms to us that Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ transcends time. There is no before or after with respect to Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ. He just is and always will be.
Time is a creation of Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ, and His perception of it is unchanging. As Imam Ghazali mentions, "only changeable things participate in past or future because past or future are temporal expressions." So Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ can't be understood according to the laws of physics He has bounded creation by. He transcends the nature of what He created and is not constrained by it. The mind is incapable of understanding what this truly means as itself is created by Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ and is limited by its very nature.
The prospect of Allah's non-existence seems completely irrational. To expand on Ghazali's thought, "He is the existent whose existence is necessary in itself." It is inconceivable to imagine how something could manifest itself out of nothingness. His existence is, therefore, essential for life, its sustenance, and the giver of its purpose.
maa ‘indakum yanfadu wa maa ‘indal laahi baaq; wa lanajziyannal lazeena sabarooo ajjrahum bi ahsani maa kaanoo ya’maloon
"Whatever you have will end, but what Allah has is lasting. And We will surely give those who were patient their reward according to the best of what they used to do." — (Qur'an 16:96)
(26) Kullu man ‘alaihaa faan (27) Wa yabqaa wajhu rabbika zul jalaali wal ikraam
"(26) Everyone upon the earth will perish, (27) And there will remain the Face of your Lord, Owner of Majesty and Honor." — (Qur'an 55:26-27)
The believer benefits from knowing that Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ is al-Baqi. We realize the best thing for us is to worship Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ and seek His approval. All else that is perishable disqualifies itself from being praiseworthy.
This is something the sorcerers in the story of Musa (as) realized. Firawn had gathered the best magicians in the city to disprove the magic Musa (as) had presented. They challenged him, "Some sorcerers stepped forward and challenged Musa (as), "O Moses, either you throw [your staff], or we will be the ones to throw [first]" (Qur'an 7:115), and in the following ayah, "[..] they presented a great [feat of] magic." Next, Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ inspired Moses, "'Throw your staff,' and at once it devoured what they were falsifying. So the truth was established, and abolished was what they were doing. And Pharaoh and his people were overcome right there and became debased." (Qur'an 7:117-119).
(72) Qaaloo lan nu’siraka ‘alaa maa jaaa’anaa minal baiyinaati wallazee fataranaa faqdimaaa anta qaad; innamaa taqdee haazihil hayaatad dunyaa (73) Innaaa aamannaa bi Rabbinaa liyaghfira lanaa khataayaanaa wa maaa akrahtanaa ‘alaihi minas sihr; wallaahu khairunw wa abqaa
"(72) They said, “Never will we prefer you over what has come to us of clear proofs and [over] He who created us. So decree whatever you are to decree. You can only decree for this worldly life. (73) Indeed, we have believed in our Lord that He may forgive us our sins and what you compelled us [to do] of magic. And Allah is better and more enduring. " — (Qur'an 20:72-73)
The sorcerers became confident in Allah's existence and realized that the promises of Firawn were temporary and futile compared to the rewards of Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ who is more enduring. Similarly, we recognize the opposite may be true, and the punishment of Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ could be more lasting than the punishment of Firawn, "And whatever thing you [people] have been given – it is [only for] the enjoyment of worldly life and its adornment. And what is with Allah is better and more lasting; so will you not use reason?" (Qur'an 28:60) This is similar to how Prophet Yusuf (as) made a du'a saying, "My Lord, prison is more to my liking than that to which they invite me [...]" (Qur'an 12:33). His faith in Allah's promise was so strong that he would rather go to prison being righteous than committing sin and being free. He recognized the rewards of Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ are far better and more everlasting than any temporary pleasure incited by shaitan.
Abu Huraira reported Allah's Messenger (ﷺ) as saying: Allah, the Exalted and Glorious, said: The son of Adam displeases Me by abusing Dahr (time), whereas I am Dahr (time)--I alter nate the night and the day. 
It is said in this hadith that the Prophet ﷺ told us to not curse time. What is meant by time here? Time is reality, the unfolding of current events. Everything that happens is by the divine decree of Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ. By cursing what has happened you're complaining about what Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ ordained. As the hadith mentions, this is displeasing to Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ, and this reaction should be avoided. If something breaks, there's no point in verbally expressing discontent about what has already happened. The mind should automatically go to saying, alhamdulillah, and figure out the next best step. Don't suffer twice by lamenting what transpired and relieving the pain.
Abu Sa'id al-Khudri reported that some people from among the Ansar begged from the Messenger of Allah ﷺ and he gave them. They again begged him and he again gave them, till when what was in his possession was exhausted he said: Whatever good (riches, goods) I have, I will not withhold it from you. He who refrains from begging Allah safeguards him against want. and he who seeks sufficiency, Allah would keep him in a state of sufficiency, and he who shows endurance. Allah would grant him power to endure, and none is blessed with an endowment better and greater than endurance. 
With regards to our connection with this name, it's limited as our life is finite. However, there is a blessing in meditating upon this. We shouldn't procrastinate as the concept of forever is only for Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ. As cliche as it sounds — and perhaps with the explanation of the name al-Baqi — we realize there is no better time for change than now. We should work towards bringing an end to destructive or unhealthy habits and promote good ones. The thing we should exhibit permanence in is our imaan (faith).