In aid climbing this is still sending since hanging on protection is part of the game (as @StrongBad points out, hanging on the rope is a little different than hanging on protection.)
In sport climbing, however, there is no specific word or phrase. I think the most common ways to describe it are:
As in "I'm projecting Era Vella 9a." This doesn't capture the fact that you've done all the moves, but most sport climbers are focused on the clean send, and so a large part of projecting involves doing all the moves in sequence with the occasional hang.
Worked through all the moves
As in "I worked through all the moves on Predator 5.13b." This could mean that you rappelled in to try each move, but in some groups this will be understood as ground-up climbing.
...but not clean.
As in "I climbed my first 5.8 today, but not clean. I had to take once after the crux." This will usually be followed by rude people reminding you that you didn't "actually send", and nice people reminding you that you should climb however you want as long as its safe and fun.
Edit: I changed the example here from "sent" to "climbed" because after thinking more about Adam's comment, I think there is a whole connotation involved with "sending" that some climbers may not like appropriated.
I think it's important to realize, though, that not officially "sending" is no less impressive or cool than sending. My experience in sport climbing circles is that no matter how hard you send or how many times you hang, other climbers will be stoked for you if you're trying hard and enjoying yourself.