As the others have noted, you don't need a copyright statement to establish your copyright. There are numerous explanations on the web and in books (I like the Nolo series), but everyone should be familiar with the US Patent Office site (which is where to go to search and register trademarks, too)
https://www.uspto.gov/ip-policy/copyright-policy/copyright-basics
but it's not a bad idea to make clear this is your work and you retain rights to it. For that reason, I think the copyright statement should have a legal entity name, whether it's your registered company name or your name, as mentioned here
https://www.nolo.com/legal-encyclopedia/when-do-you-need-copyright-notice-softwa...
As for credits, this is less important, but I think if you have a credit list or credit screen, you should also use your real name, as those lists end up in sites like mobygames and you want both some consistency (if I go on mobygames and enter my name, hopefully everything I worked on will show up), and also unambiguous attribution if some dispute occurs. That might seem like a remote danger, but I have received numerous complaints about the original credits for a game I did a licensed remake of, and those credits were from twenty years ago! So I am all in favor of credit standardization like they have in Hollywood and as proposed by the IGDA (although they haven't updated their proposed guidelines since 2014).