Need to Resync Time Machine to a backup folder with my history

Somehow Time Machine has renamed the backup folder I've been using for years and wanting to do a whole new first complete backup

which I don't want. Is there a workaround for resyncing to that history? What's odd is when you enter into Time Machine, everything seems

connected to my history and you can scroll through, but it says it's waiting to to complete first backup which I'm afraid to allow.