Sounds like a problem of the branded Contacts app. Unfortunately, many Contacts apps assume that there can be only local and Google contacts 😕
If you really need this, you could try another Contacts app or a custom ROM like Linage.
assume I have an CardDAV account named “account” with an address book called “Accounts Addresses” (Baikal server, if that matters).
I my contacts app I now see something like “Accounts Addresses (account xy)” in the address book selection. What is that “xy”? It seem to be 2 random letters (containing uppercase/lowercase/numbers).
Please see here: https://www.davdroid.com/manual/accounts/#c272
DAVdroid address books accounts: They’re named after the CardDAV address book which they are connected to, plus a hash of the URL, for instance: My addresses (UA). The hash is necessary when there are two address books with the same name. The address book account names will be shown in your contacts app as possible destinations for contacts.
Without the hash (the two letters), it would not be possible to have two address books with the same name (e.g. “Address book”) in two different CardDAV accounts.