Founder of filmschoolsecrets.com, Producer/Writer of upcoming feature film "Wally Got Wasted".
A standard cover page should have the name of the movie, authors, and you can put a date of the draft, email, phone etc. That's all you really need.
I'll nerd out on this a little because I had to research it over the years.
Copyright is an often misunderstood concept. Once you write something and make it real, i.e. put it on paper it is technically "copyrighted". You can go to the US Copyright office website copyright.gov to make it official (and by the way you'll need that if you ever shoot something yourself when it comes time to get insurance/title clearance).
What I do suggest is registering the script with the Writer's Guild. https://www.wgawregistry.org/ Not really legally binding but it's an industry practice and good for determining the time when something was written.