I think I know what you mean. By "name" do you mean Login ID?
If so, I'm sorry to report that there is no way to do it. I've complained to them before and they always claim they don't allow it for security purposes. You need to gather all the required infomation and fill out the account change form. Half the time, my customers don't get the GoDaddy emails due to SPAM filters. It's a pain in the @#$.
I've got a lot of domains at Enom and pushing domains to new account is so easy, you just type in their username and you're done.