Well, as you say, any one of those three could be shortened to Ann.
What you need to do is start looking for records of any of those three names which would be INCONSISTENT with their having been George's mother.
If you're lucky, you'll be able to rule out one. If you're exceedingly lucky, you'll be able to rule out two. If you're exceedingly unlucky, you'll be able to rule out all three.
The kind of things you're looking for is marriages, especially if followed by census entries showing them somewhere else altogether following marriage; deaths; baptisms of children both before and after George where the full, unshortened name has been used (but check that there is not a change of minister to account for the change in style); baptisms of children at about the same time as George but in a far distant parish.
Then you could see whether any wills exist which may help to resolve it.
There are ways to attack this problem ... but the key point is that you need to chip away and chip away, removing one layer after another, until there is only one plausible candidate remaining.
(You may never achieve that, of course ... but keep hold of all of the evidence you can find, and review it from time to time, and maybe another potential line of enquiry will occur to you ...)