I misread a question from commenter Comedy Gaz, so let's try it again. (Good thing I held one last Suggestion Box Monday of the year in reserve.)
Okay, first of all, "Why would you want to do this?"
I see no explanation for how this could possibly escape the 100-point hole every feature starts out in. I mean, these are items you deleted. Why do you care what their names are? Are you renaming it so you can find it again later? Why would you go to the effort of locating an item in the Recycle Bin, and then not bother recovering it? It's like calling the Lost and Found at Grand Central Terminal, and saying, "Hi, I left my umbrella on the Danbury train last Tuesday. It's blue with white snowflakes. Yes, that's the one. No, I don't want to come in and get it. Could you just dye it green, and paint a yellow smiley face on it? Thanks."
The purpose of the Recycle Bin is not to provide another place where you can organize your data. The purpose of the Recycle Bin is to give you one last chance to recover the data you deleted by mistake!
What would be the point of writing the code to allow the name to be edited, update the name in the Recycle Bin databases (watch out for the cross-process race conditions!), then locate all the other open Recycle Bin windows and tell them, "Hey, if you were showing the name of deleted item number 51462, please go refresh it, because it has a new name"? That's a lot of code to be written and tested (and re-tested every build) for a pretty dubious scenario in the first place. (And why stop at just the file name? Why not let people edit the Original Location and Date Deleted too?)
From an information-theoretical standpoint, renaming an item in the Recycle Bin would be a falsification of the historical record. The information about the items in the Recycle Bin describe the item at the time it was deleted. Its name, the folder it was deleted from, the date it was deleted. If you could change the name of an item in the Recycle Bin, then that record would be incorrect. "This icon represents the file that you deleted from folder Q, except that the name I'm showing you isn't actually the name. It's some bogus name that somebody edited."
It'd be like asking the church to go update its registry to change your birth name. "Yes, I know that I was
born baptized with the name Amélie Bernadette, but please change your files so it says that I was baptized with the name Chloë Dominique. Thanks."
The church isn't going to do that because that would now be lying. You were baptized with the name Amélie Bernadette. You are welcome to change your name to Chloë Dominique, but that doesn't change the fact that you were baptized with the name Amélie Bernadette.