Multiple sets of time machine backups on the same drive

I want to know if I can have multiple sets of time machine backup files on the same external drive.

My wife's MacBook Pro had become terribly bogged down with all sorts of junk. So, I recently wiped my wife's hard drive (using Disk Utility Erase), reinstalled the OS, and reinstalled only those components that she still uses. HUGE improvement in performance! Before I wiped her drive, I backed everything up to time machine.

Now that she has a reinitialized and cleaned up hard drive, I want to begin a NEW set of time machine backups without losing the backups of the old set. However, the computer has the same name as before ("Jane Smith's Computer"). I don't want Time Machine to overwrite her backup file with a new one of the same name. I tried this several years ago and I lost all the old backups.

My question is, can I "map" her Time Machine backups to a unique folder that will be used in the future?

For example, her old backup files are here:

Time Machine Backups > Backups.backupdb > Jane Smith's Computer

I'd like to backup from now on to this folder:

Time Machine Backups > Backups.backupdb > Jane Smith's Computer after 4/25/15

(I wish I could just rename her old backup folder, but Time Machine won't let me rename the folder.)

Does anybody know if this is possible? Bottom line: I don't want to lose her old backup files when I hook up her "new and improved" hard drive to Time Machine backups.

Thanks in advance,

Greg