Is there a way to merge Time Machine backups?
You can still access data from "dee's backup" by selecting "Browse Other Time Machine Disks" from Time Machine's Dock menu. (Right click or click-and-hold on TM's icon in the Dock.)

TM is holding onto both sets of data because even though YOU know you copied all the data from the old machine to the new, all TM knows is that a bunch of data just showed up on the new machine. It doesn't know where that data came from, but knows it should be backed up.

When TM, running on "dee's Macbook Pro", needs to delete files to make room, it can only delete files backed up from "dee's Macbook Pro". Even the root user on that machine has no authority (and cannot give TM authority) do delete some other computer's backup files.

You don't need any of "dee's iMac" backup. As you say, everything from that computer got copied over, and none of it has been needed since last year. It's time to let it go. To do that, open the Backups.backupdb folder on your backup disk, and delete the subfolder named "dee's iMac". (I'm assuming you're backing up to an external disk connected to your MBP. Details will be different if you're backing up to a Time Capsule or a network volume, but the principle is the same.) Time Machine won't let you modify that backup in any way except that it will allow you to delete it in its entirety. You'll need to authenticate as an admin to do that. And it will take a while. You should be able to delete it using Finder, but if not you can enter the Terminal command:

sudo tmutil delete /Volumes/"disk name"/Backups.backupdb/"dee's iMac"