What's in a name?

Factual Questions
1

In “Back to the Future III”, Marty (Michael J. Fox) uses the name Clint Eastwood while in 1885.

Did the producers of BTTF3 have to get any permission to use Eastwood’s name like this? Or are names public domain?

Does anyone know what Clint thought about it?

2

But surely Clint Eastwood needs Micheal J Fox’s permission to use that name since chronologically he thought it up first - or did he ?

3

Clint Eastwood’s name is his given name, rather unique in Hollyweird. He’s a junior, too: Clinton Eastwood, Jr.

If his father was 45 years old when lil Clint was born, then Clinton Eastwood, Sr., would pre-date Marty’s Clint Eastwood.