From a generic, non-specific, automatic mail on behalf of the company? Which everybody gets? If it was private between me and her you'd have a point.

She included her name, I didn't, and I don't see harm in repeating the mail verbatim.

The thing that struck me about the emails in question was that by including the name, it makes it more personal, which makes it seem as though they are trying to presume a closer relationship than they actually have, which makes it seem scammy.