@kaymartian This is my 4 cents (inflation ya know). Back in the old days, I think before 2005, you could enter a name you go by on a SSA application. Like Bob for Robert or a middle name. Since the birth certificate listed both names that was acceptable. Then it became legal name, which is first name.
Now, the vaccine provider should be wrong about having to put insurance name. They should put legal name. Insurance is just what they use to bill the provider for the administration of the vaccine. Insurance also has your id number, SSN and birthdate to verify it is you (not all of it on the card but it is proof in their records for billing that it is you). There should be a database where this info is submitted and provider that gave you the card should be able to edit and re-issue card. Or someone should have some knowledge of your predicament. I don't know what to say if you can't get those that do that to help.
However, all the documents you have should provide proof of who you are with birth certificate having both first and middle names along with differing documents you have with Mickey and Lynnette in various forms on them. If you can not have the card/database record changed, then ask the intended travel people if your other documents as a whole or which ones could be accepted as proof it is you and the vaccine card is yours as well.
I don't know if this helps any, but I wanted to at least try. Good luck.
