If bank accounts are not in my mothers trust is it OK to have my name on her accounts?

This is question is a little difficult. There are valid reasons to "fund" trusts and valid reasons not to "fund" trusts. Without speaking to your mother I am unable to ascertain her estate planning goals. As to the legality of placing your name on accounts outside of trust it is permissible with your mother's permission. If the accounts are within the trust you need to be a co-trustee.