Should I amend my taxes if my last name differs from my spouses last name, filing jointly?

No.  That is not a reason to amend your tax return.  It is common now for a wife to retain her maiden name and not change it after marriage.  If you did change it, make sure you have changed it with Social Security so that your SS records will match the name you are using.

you should use the last names that Social security has.   if you kept your last name after marriage and that's what your using then that's what should be on the return.  if you desire to use your spouses last name, you need to change it with Social Security and that would be what should be used on the return.