It's really up to you. The fics are only anon until the New Year.
If it bothers you that people might guess who you are, don't include the beta and thank them once the authors are revealed. Or you could say something like "Thanks to my beta who frequently works with me. You know who you are." I know I personally would be okay with that if my name was already mentioned in the author's other fics.
If you're worried about offending your beta, you could always ask them which they would prefer.
Some people may also not be bothered enough to really try to identify their author anyway, or are unlikely to recognize someone based on that. So it's up to you really.
Author's notes will be revealed with the fic though, for anyone wondering about that. Only the author name won't be revealed.
Re: Secret Santa
If it bothers you that people might guess who you are, don't include the beta and thank them once the authors are revealed. Or you could say something like "Thanks to my beta who frequently works with me. You know who you are." I know I personally would be okay with that if my name was already mentioned in the author's other fics.
If you're worried about offending your beta, you could always ask them which they would prefer.
Some people may also not be bothered enough to really try to identify their author anyway, or are unlikely to recognize someone based on that. So it's up to you really.
Author's notes will be revealed with the fic though, for anyone wondering about that. Only the author name won't be revealed.