was/in

[Silverobama]

Hi,

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

[Raymott]

Hi,

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.