Nope, I waa able to do it.
First, the SSA allowed my Wife to change her middle and last name per the Philippines custom. Though, they didn’t seem to care what we chose for a name.
I then asked them to swap my first and middle last name to match my passport, DL, etc… Previously they told me I needed a court ordered name change for this. But now they agreed to do it based on the marriage certificate which had my first name swapped just like my passport. I then received a new SSN card with my first name changed