Maybe your contacts are being merged together on Android from different sources (thats what Android normally does if there are same numbers synced from Fastmail and you had some numbers on the phone in a different account like the SIM card or on Google contacts). So if you then edit a “merged” contact normally you can choose where it should belong to and if you select the DAVx5-Fastmail-addressbook from the dropdown in the contacts editor then it should sync back to Fastmail. If there is no option to choose then thats maybe the problem.
In order to get rid of a chaos: make sure fastmail has all your relevant contacts. Then delete the DAVx5 account (don’t flag the contacts itself as “deleted” becaus then on next sync the delete request will be performed on Fastmail and your contacts will also be deleted on fastmail).
After removing the account delete all remaining contacts and entries from your device. After that create the DAVx5 with fastmail again and synchronize the address books you want. At least then changing/adding names should work. Btw on Android it is not allowed that contacts have “no” name. So all contacts must have a name… Hope that helps…