Rosmerta - First or Last name

[Lea]

No: HPFGUIDX 128608

Had an interesting conversation with another HP friend of mine about 
Madam Rosmerta.  I've always thought that Rosmerta was her last name, 
and was surprised to find out others think it is her first name. So, 
I'm wondering what your opinions are?

My reasoning for believing this to be her last name:

Madam Pomfrey (Poppy Pomfrey),  Madam Pince (Irma Pince), Madam Hooch 
(Rolanda Hooch - HP Lexicon, from trading card game), Madam Edgecombe, 
Madam Malkin, and Madam Marsh, all obviously last names.  So why would 
Madam Rosmerta be different and be a first name?