Does 上鳴 mean shut up? I didn't find a good meaning of this in the dictionary.
No, if you're still reading/watching 僕のヒーローアカデミア My Hero Academia, then 上鳴【かみなり】 is the name of a character in that manga/anime. (Being a proper name, you wouldn't find it in a dictionary — of course it's a pun on 雷【かみなり】 "thunder/lightning" which you will find in a dictionary.)
that is character's name. and the words 上鳴 there is no meaning. just a pun.
other character's also.
飯田天哉（iida tennya）his ability is engine(fast leg) his name came from 韋駄天(idaten) one of the god in japan.
八百万百（yaoyorozu momo）his ability is create(make a lot of things). her name came from 八百万の神（yaoyorozu no kami）in Japan, there are a lot of god. the god of water, the god of tree, the god of fire, the god of chair, the god of table...even it is artificial things, there is god. and she can make these things by her ability.
like this other character also has the meaning.