We are seeing a few people on Catalina having issues with Time Machine.
To actually change the name of sparsebundle to backupbundle would be surprising but perhaps is clearer terminology.
Can you post some details for me.
Did Catalina actually change the name of the existing sparsebundle or is the backupbundle actually a new backup.. Just check and see if the old sparsebundle is still there.
If you cannot mount it in finder the most likely cause is permissions. It is possible Apple has done more than change the name.. this is ongoing to prevent ransomware from encrypting your backups (total guess).
I can get you around the permissions issues.. or you can try yourself using get info in finder. There is a trick to do it from old airport utility 5.6.1 but I am not sure it has been modified for Catalina yet.
Time Machine has become poorer and weaker and more problematic since Sierra.
My first recommendation is to stop using TM and use a third party. I recommend Carbon Copy Cloner. (purely a user, no connection to the company).
If you really MUST get Time Machine working again.. I would archive off the TC.. assuming you want to keep the old backups, then erase it and reset it to factory. Do the setup again of the TC from the computer you have issues with.. Use short names, no spaces and pure alphanumerics. NOT the apple recommended names which are hang over from early days of AFP only. The Mac is now using Windows network protocol, SMB, but the TC was never upgraded.. and this does lead to problems.
If you still have issues after doing all that give me details of the network setup. Model and age of the TC might also be relevant.