The Guarding One, The Protector, The One who Preserves what He created.
Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ is Al-Hafiz (in Arabic: ٱلْحَفِيظُ), the guardian and protector of everything. He preserves all creations and remembers all that has ever been and all that is. He is the protector of The Qur'an and vowed to safeguard it from being changed or perverted, as was the case with previous scriptures.
From the root ha-fa-za (ح ف ظ), which has the following classical Arabic connotations: to preserve, guard, protect, to keep, retain, take care of, tend to, prevent from perishing, or becoming lost, to be watchful, mindful, attentive, and vigilant.
Al-Hafiz - The Protector:
The name of Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ Al-Hafiz (other common transliterations include Al-Hafeez or Al-Hafeedh) appears for a total of six times throughout the Qur'an. There are different aspects of this name we can explore. Imam al-Ghazali writes the first is "perpetuating the existence of existing things and sustaining them, the opposite of which is annihilation." In this light, we see Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ as the preserver in the sense of being a protector. A name that shows trust in Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ plan for us and humanity as a whole. Every parent dropping their kids off at school, every person caught amid a war or dangerous situation. Or it could be something as simple as entrusting something valuable to someone else; the attribute of Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ we need to know is that He is Al-Hafiz. Sheikh Tosun Barak writes, "He protects His creation from all harm and disharmony. That is how all heavenly bodies speeding in great haste revolve and travel within their destined orbits, instead of clashing with each other." This is the work of Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ as being Al-Hafiz.
"So exalted is Allah when you reach the evening and when you reach the morning. And to Him is [due all] praise throughout the heavens and the earth. And [exalted is He] at night and when you are at noon. He brings the living out of the dead and brings the dead out of the living and brings to life the earth after its lifelessness. And thus will you be brought out." (Qur'an 30:17-19)
The Perfect Balance:
Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ has perfected the balance of the elements and instilled self-preservation within all creation. All things are instinctually guided. This is how birds know to migrate south for the winter, how bees can travel 12km away from the hive and find their way back, how salmons return to the same river bank they were born to lay their eggs despite having traveled hundreds to thousands of miles away in the vast ocean. It's jaw-dropping to consider how different elements that are at odds with one another (e.g., hot and cold, dryness and wetness) exist under our skin in the perfect balance because Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ has reconciled them to be that way. The human body is a powerful self-regulating system. If you look at the average body temperature in humans, it exists within a small range of 36.1 C - 37.2 C. The same is true of our blood pH level, hovering around 7.35 to 7.45. The slightest diversion from this range can have very harmful effects. Yet, within our body, the pH level of the acid in our stomach is 1.5-2.5. If this came in direct contact with your skin, it would burn a hole through your flesh. But Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ — great and glorious — made it so our stomach can safely house this acid for self-preservation to help eat and digest food.
Fa in tawallaw faqad ablaghtukum maaa ursiltu biheee ilaikum; wa yastakhlifu Rabbee qawman ghairakum wa laa tadur roonahoo shai’aa; inna Rabbee ‘alaa kulli shai’in Hafeez
But if they turn away, [say], 'I have already conveyed that with which I was sent to you. My Lord will give succession to a people other than you, and you will not harm Him at all. Indeed my Lord is, over all things, Guardian.'" — (Qur'an 11:57)
Innaa Nahnu nazalnaz Zikra wa Innaa lahoo lahaa fizoon
"Indeed, it is We who sent down the Qur’an and indeed, We will be its guardian." — (Qur'an 15:9)
You may be familiar with the idea of reciting Ayatul Kursi if you're afraid and want some kind of protection. But why else do we recite Ayatul kursi? What's special about this verse? In the tafsir of Abul Ala Maududi, "A fundamental fact about war – that victory and success do not depend upon superiority in either numbers or weapons – was then indicated. They depend rather on faith, fortitude, discipline and firm resolution." This is the idea that nothing can happen except by Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ permission. In moments of complete despair, when it looks like you can't win the battle because you're outnumbered - the one who can grant you victory, provide protection, and bring you comfort is Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ. Believe in Him, praise Him, call upon His attributes, "Ya Hafeedh, Ya Maani, Ya Qawwiy, Ya Aliyyul Azeem" - "O Guardian, O Preventer of Harm, O Strong One, O Most High, the Most Great" and continue asking for whatever you wish, "guide us, forgive us, grant us a safe passage."
Qaala hal aamanukum alaihi illaa kamaa amintukum alaaa akheehi min qabl; fal laahu khairun haafizanw wa Huwa arhamur Raahimeen
"He said, 'Should I entrust you with him except [under coercion] as I entrusted you with his brother before? But Allah is the best guardian, and He is the most merciful of the merciful.'" — (Qur'an 12:64)
We can make du'a in any language, but another reason for reciting Ayatul Kursi is given in the hadith. narrated 'Abdullah bin Mas'ud: "Allah has not created in the heavens nor in the earth what is more magnificent than Ayat Al-Kursi." Sufyan said: "Because Ayat Al-Kursi is the Speech of Allah, and Allah's Speech is greater than Allah's creation of the heavens and the earth."  So, with this perspective let's review this magnificent verse.
Allahu laaa ilaaha illaa Huwal Haiyul Qaiyoom; laa taakhuzuhoo sinatunw wa laa nawm; lahoo maa fissamaawaati wa maa fil ard; man zal lazee yashfa’u indahooo illaa bi-iznih; ya’lamu maa baina aydeehim wa maa khalfahum wa laa yuheetoona bishai’im min ‘ilmihee illaa bimaa shaaa’; wasi’a Kursiyyuhus samaawaati wal arda wa laa Ya’ooduhoo hifzuhumaa; wa Huwal Aliyyul Azeem
"Allah – there is no deity except Him, the Ever-Living, the Sustainer of [all] existence. Neither drowsiness overtakes Him nor sleep. To Him belongs whatever is in the heavens and whatever is on the earth. Who is it that can intercede with Him except by His permission? He knows what is [presently] before them and what will be after them, and they encompass not a thing of His knowledge except for what He wills. His Kursi extends over the heavens and the earth, and their preservation tires Him not. And He is the Most High, the Most Great." — (Qur'an 2:255)
The verse does not explicitly state the name Al-Hafeedh but mentions Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ as being watchful over "the heavens and the earth, and their preservation tires Him not." which encompasses the same attribute as the name Al-Hafeedh. It also calls upon Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ by many names which we have covered up until this point. Can you identify them? 
Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ has provided the answers to things that threaten our existence and our harmony and taught us how to be protected from them. He sent this through His books and His teachers (i.e., the Prophets, may peace be upon them). He tells us to be cautious and avoid the poisons of gambling, alcohol, adultery, backbiting, envy, jealousy, and ignorance. He advocates for charity, lawful marriages, looking after your community, seeking knowledge, become intelligent and useful. He's not denied us enjoyment and complete detachment from all things. We're encouraged to enjoy what's permissible while keeping our duties and responsibilities.
By studying the name Al-Hafeedh, it should inspire us to further rely upon Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ. We should seek to mimic this attribute in small ways, to give our best effort to memorize the Qur'an and become a Hafiz. This is probably too big of a task, so break it down and be a "preserver" of a few small surahs. Narrated Abu Hurairah: The Prophet ﷺ said: "The one who memorized the Qur'an shall come on the Day of Judgment and (the reward for reciting the Qur'an) says: 'O Lord! Decorate him." So he is donned with a crown of nobility. Then it says: "O Lord! Give him more!" So he is donned with a suit of nobility. Then it says: "O Lord! Be pleased with him.' So He is pleased with him and says: "Recite and rise up, and be increased in reward with every Ayah."" 
We must also try to preserve our deen and our character from being corrupted by sin. The Shaitan will try to pull us in many directions. He will encourage us to get angry about small things, to let down over here, and to give in to some temptations over there. We must actively fight to preserve our faith. We should also seek to preserve things encouraged in Islam, kindness to one another, love among the community, and keeping the peace. The only justification for fighting is against oppression and tyranny.
 Sahih (Darussalam) Jami at-Tirmidhi 2884
 Five names: Allah, Al-Hayy, Al-Qayyum, Al-Aliyy, Al-Azeem. However, attributes such as His decree, knowledge, and dominion are also referenced.
 Hasan (Darussalam) Jami` at-Tirmidhi 2915