Plenty of girls get a family ln as a mn - I know a
Barbara Watson Ln, a
Caroline De Villiers Ln and probably others. So, yeah, that's what the mn slot is for: family names.
But if you wanted to give her a longer version that could be shortened to Glen(n), there's always
Glenda or
Glenys. I knew a Glennifer at university, but I don't advise it.