This is my first time filing my taxes, got rejected because of my SSN and last name not matching and now I can’t fix it because it’s too late. My only option to file is mail now but has some

Late has nothing to do with e-Filing. You have till Oct 15

If you can't e-File, file on paper via US  mail

But I made a mistake on my last name and middle name. They’re switched and forgot to mention about my Roth IRA contribution as well. Then what do I do?

If you have not filed you can go back in and fix it and enter the ROTH contribution.
Click on Add a State to let you back into your retun.

You can still fix it and resend it until Oct 15.  Being late should not prevent you from Efiling.