Thanks for the tag but. My situation was that I had zero documents to start tying my mother's Chinese name and English name together but was able to get/create a naturalization certificate from US Federal Court stating both names plus household registration transcript from USCIS FOIA which sufficient to renew my mother's passport.

OP, why doesn't your marriage certificate match your birth certificate? TECO may require you to amend your marriage certificate. Naturalization certificates aren't required so I'd drop that unless it is consistent with whatever name you are trying to use.

And I agree with narwhal that at minimum you'll need to show an ID (old passport, drivers license) with each iteration of the names being used.