I don't remember what her name was—my memory is a little foggy.
I don't remember what her name is—my memory is a little foggy.
Are these two sentences both grammatically correct? If so, what's the difference?
Thanks a lot
They are correct, and in most cases would mean the same.
You should be able to think of a situation in which the woman's name is not the same as it used to be, thus making the sentences have different meanings.