Patricia, good morning and my apologies - we lost power due to the Blizzard thing going on, but I am back on.
Yes, you can cancel you application if it was never approved - first and foremost. But that said, you are going to want to get your names connected - ie. use only one on legal documents.
You indicate your marriage certificate (you said license, but license is not the resulting cert.) has the same name as your birth name? Did you marry a guy also named Canterbury?? Or is his name Montgomery? Because it is is, that is your legal doc to propose Montgomery as your legal name, after being born Canterbury - that connects those dots. Then, you may have deviated a bit by using "C" as your middle inititial rather than A on your DL. I'd go and get my DL fixed and then go get my SS card fixed, since now you will have connecting documents to prove who you are.
I don't blame you for not wanting to mail your docs - but that does mean you need to go in person. It is not clear to me WHAT local office refused you, but it may have been because your documents simply do not match or connect and therefore you are unable to prove you are the same person throughout. Once you get your documents corrected to tie together, you can get the SSA to recognize you.
I realize this will take a few weeks and you may want to file before then, but remember that the longer you delay taking between now and age 70, you INCREASE your benefit forever. If you could get by to 70, your age 66 benefit would jump up 32%. But even just a 1 year wait gives you an 8% raise in benefit.
Anyway, it is what it is - many of us are having to get our ducks in a row with new rule on how to establish identity in this post 911 era. Your situation is not nearly so harsh as many, some of whose paperwork is so backwards they can not get these renewals with corrections.