Is there a name for arguing with other people in one's mind?
I'm not aware of a term specifically for this phenomenon.

Having a conversation in one's head has been termed dialogic inner speech by several researchers.  You didn't mention if the people you are arguing with reply back - if they don't, then it's just regular (monologic) inner speech.

One common function of inner speech is sometimes referred to as speech rehearsal - ie, where one might practice a monologue or dialogue (eg, debate) in their mind ahead of time.

In a more pathological context, repeatedly looping through a conversation in one's head can be a form of rumination, and simulating a future argument could be considered action rumination if it is a reaction to a recently failed argument.