Because of the incorporation of iPhone and Apple Pay into the process, I suspect the ID verification process may be stricter. Here are a couple of articles that may help,
https://support.apple.com/en-us/HT207887
https://support.apple.com/en-us/HT204164
Basically everything in the process has to match. This includes,
1) Apple Card application including legal name, current address, birthdate/age, social security number etc.
2) State Issued Drivers License/State ID — must not be expired
3) TransUnion Credit Report
4) Apple iCloud Account/Apple ID
If everything matches, contact Apple Support (not Apple Card support) and ask for help with your Apple ID so they can verify everything on the Apple side and help fix if necessary.