First thing first; it's up to him and it's his right to choose his own wardrobe. I can say he should, but it's absolutely his decision whether or not he'd do it for real, no? I do think that the idea of a Glover wearing gloves all the sounds 'pun'ny and iconic for one. So, I support the idea.
Glover would become well known if he wore gloves all the time. His life could be a pun as well as his professional career. Everyone would know him for that one thing. He could get a bunch of different types of gloves and people would always wonder what type of glove he was going to wear next.
To make a celebrity wear something that is their "namesake" all the time seems odd and silly. Donald Glover has many accomplishments and is a respected actor. It would quite possibly ruin people's ability to take him seriously if he were to begin wearing gloves all the time, simply because his name is Glover.
As a citizen of a free country, Danny Glover has the right to choose to wear whatever article of clothing he likes without regards to what his last name may or may not indicate. Since having bare hands would not violate any nudity laws, his choice to leave gloves out of his wardrobe is perfectly acceptable.
Danny Glover should not wear gloves based on his last name. That would be absolutely ridiculous and come across and a simple and childish attempt. Mr. Glover does not need a gimmick to be remembered. He is an accomplished and memorable actor in his own right and will be recognized for simply that.