Is it a problem if a Medicaid applicant's name is listed on accounts of her daughter?

Yes it is going to be a problem if she has access to the money. Most state workers don't have the training or policy behind them to disregard the other party's money if the applicant could spend it all on their own needs.

Yes it is, if by that you mean the account is a joint account with her daughter's money. If she is just a signer on the account, but the account is not titled to her, it's probably not a problem. Ask the band how the account is titled.