Your confusion lies in thinking, as you've said, "just a new version of a language." It's actually been a long, 15-year journey that resulted in a completely brand new language. The name is still 'Perl 6' for historical reasons, but it may as well be called 'Rakudo'; something people've not heard of yet. The Perl 5 language is still being developed and improved, with a major release every year. Hence, the filename distinction.
However, it's just a convention. You can have any extension you like (at least on *nix).
And to answer your question, no "use v6" is not mandatory. It's there so if you run your script with a perl (and not perl6) interpreter, you won't get confusing errors.
Of course one can have any extension. Not that it's a bad thing to use .p6. I was just trying to make it clear for myself to understand how beneficial the new extension is. Part of that lies in "marketing" the language. Old school engineers may still want to use .pl, whereas newbies will follow the documentation and have their files prefixed with .p6. My worry is that such behavior may lead to a confusion in Open Source world and push away newcomers from using the language.
I've been following the journey for, more or less, the past 10 years. I hope that whoever spent those 15 years on developing Perl 6, will reap the rewards.
However, it's just a convention. You can have any extension you like (at least on *nix).
And to answer your question, no "use v6" is not mandatory. It's there so if you run your script with a perl (and not perl6) interpreter, you won't get confusing errors.