Is there a way to merge Time Machine backups?

Last year, I switched from an iMac to a MacBook Pro, and I restored from my Time Machine backup. I've been using Time Machine since then, and never checked it until now. I just found out that my backups are split into 2, "dee's iMac" and "dee's MacBook Pro" when I expect them to be just one backup since I moved everything from my iMac to MBP.

The "dee's iMac" backups aren't accessible through "Enter Time Machine" and aren't deleted when Time Machine is full; instead, it will delete the newer backups from my MBP backups, which currently holds only the past 2 months while there are backups from my iMac from last year.

Is there any way to merge these backups? What happens if I just move all the contents of the "dee's iMac" folder to the "dee's MacBook Pro" folder? Or should I just delete the entire "dee's iMac" backup folder?

Note: Currently on OS X Yosemite, 2013 MBP (non-retina)