“Flynn” is the name that Walt Jr. preferred to be called by when he wanted to distance himself from his father in the earlier seasons (since they share the same name). But over time he forgave his dad and went back to Walt Jr/Junior. But when Marie found out about Walt’s criminal past, she started insistently calling him Flynn in order to disassociate him from Walt in a similar manner.
As for the inspiration behind the name “Flynn”, R.J. Mitte (actor who plays Junior) says in an interview with AMC:
I know it was an old movie star — Errol Flynn. It took me a while to figure out where it came from though. I asked Vince, “Flynn? Out of all the nicknames?” And he’s like “Well, that’s why I picked it.”
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