I don't know if the name specifics matter to the average viewer. To your average person Ironheart is the female Iron Man just like how Kate Bishop is the female Hawkeye. Ms. Marvel may actually be the exception because she was an original character who appropriated someone's name, there being an OC and a legacy character at the same time.
I don't think Miles has to fit within Peter's narrative, although I do wish they would interact more. I get the "no Spider-Man is a sidekick" shtick but Peter seems like the type to want to mentor and help Miles out as much as possible.