When you erase a drive, it gets a new UUID (Universally Unique IDentifier). That's what OSX uses to keep track of drives, not their names. So it's treated as a different disk.
If you do a full system restore, or use either Setup Assistant or Migration Assistant to transfer the data from your backups, that leaves a "trail" that Time Machine uses to figure out what's happened, and "associate" the "new" drive with the old backups. The next backup will be only an "incremental" one, of what's new or changed, and the new and old backups will all be treated as if they'd been done from the "new" drive.
However, if you restore things "piecemeal," there's no trail. Time Machine will make a new, full backup of the "new" drive. You can still see and restore from the "old" ones, via the procedure in #E3 of Time Machine - Troubleshooting.
But if you use the exact same short user names (home folder names), then you may be able to force Time Machine to "associate" the "new" drive with the old backups. See #B6 in the Troubleshooting article for instructions.