Is there a way to rename an assignment?
Not after students have started working on it.
If students have not started the assignment you can create a copy of the assignment with a new name and then delete the old one.
Not presently. The name of the assignment serves as a key in the database, so until that is changed in some future version, it is not possible.
The next best thing is to go to Hmwk Sets Editor, Create tab. You can create a new set as a copy of an existing set, and name it how you like. This copies the structure of the set, but it won't copy any student data. So there is no real solution to this if students have already started submitting answers.
Note: when you are giving a new name, use underscores where you want spaces. So name it "Homework_1" if you want it to come out looking like "Homework 1".