Synology NAS

Ensure your NAS is broadcasting the right Bonjour credential, and consider connecting with SMB to the fixed IP address of your NAS, not to its name. Ensure your NAS admin credentials and password are in your keychain

Ensure the latest DSM version is on your NAS first

All I can say is that it works for me

I made no changes to Catalina (10.15.0/1), or to my Synology NAS configuration — for it to just connect filesystems to my Late 2013 iMac. Serving multiple filesystems from the Synology as Apple File Protocol (AFP) over TCP/IP, and it just works with Catalina, as it has with preceding releases of macOS. I do not use the Synology as a Time Machine backup solution.

Because of the age of my Synology, I am not using anywhere close to the current DiskStation Management Software (DMS).

I use mine for Time Machine. There have been some hurdles to jump, and it still skips the first backup of the day (bizarre or what?) but I am content with it

I also made sure that my TM backup is connected at login in Sys prefs> Users>Login Items

Synology Admin Login > Control Panel > File Services > SMB/AFP/NFS Tab and tick the correct thing there then Advanced tab and do the same if using Time Machine

Use a scratch external device, clone your boot device into same, boot and upgrade and test with same.

Any issues, use your NAS to raise a support ticket with Synology directly. They have not fund the transition to Catalina to be smooth for all their customers