Is it ok to use names from shows/games/etc. or would that be copyright infringement?
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Depends on what names you use 
like “Bob” would be okay, but “Gandalf” would definitely be infringement xD
So just stick to basic names to avoid any trouble?
Or make up your own names
I suppose but it’d probably be best to create your own, unique names. Of course, I don’t know anything about how you’re going to implement these names, but that’s just a piece of general advice.
Legally speaking, names are not copy protected, but characters are. To elaborate, if you had a character in your work that wore glasses, had messy black hair and a scar in the shape of a lightning bolt, and waved a wand and did magic, and was named Harry Potter, that would be copyright infringement. But, if you had a character that was named Harry Potter but otherwise had no resemblance to the popular character, that would be fine, but be prepared for people to call you out on lack of creativity.
For reference