Bi-smi llāhi r-raḥmāni r-raḥīm. Here is my ideas on ayat 12 of Surah Luqman in context of why Luqman was given Hikmah and root meaning of name Luqman.
Arabic name لُقْمَان (Luqmān) from Arabic triliteral root ل-ق-م (L-Q-M), which primarily denotes the act of eating, feeding, or taking a morsel. The verb لَقِمَ (laqima) means “to feed” or “to put food in the mouth,” and the noun لُقْمَة (luqmah) means “a bite” or “a mouthful.”
The root tool or human organ for examination of any object is the Mouth. Look what babies do when they want to examine something. They put it in their mouth. You Touch, Grind (feel consistency, solidness, liquidness / softness), smell [chemicals], taste [chemical and nutritional value] while you put it in your mouth. During this process, an External object, you internalize and try to Internalize the understanding about it by Mouth Examination and Exploration.
And when you chew over the morsel of food (Lukmah), you are actually assessing the situation/object in mouth. And when you "chew over" or ruminate, it means you are thinking very deeply about something. To grind the food, you need tooth and without tooth, you are too immature to understand what is in your mouth. When you have the biggest molar to grind the best with your "wisdom tooth" you now have the maturity to understand what kind of object [food] you are dealing with.
When you Like and appreciate Sweetness and Savorieness - you eat it and when dislike and abor causticness/bitterness - you spit it out. This innate ability of discernment of good vs bad is at the root of Hikmah. And those appreciate this innate gift as a Rahmat of Allah, Allah guides you more to attain more Hikmah and you develop more and more "great teste" for it.
"Indeed, We blessed Luqmân with wisdom, [for ] saying (or who said)˺, “Be grateful to Allah, for whoever is grateful, it is only for their own good. And whoever is ungrateful, then surely Allah is Self-Sufficient, Praiseworthy.” 31-12.
May Allah grant all of us the wisdom to be more grateful so that we can attain more and more wisdom.