shabu I am guessing from your name that you are either Korean or Japanese or possibly elsewhere in East Asia. Since my husband is Korean, I do feel kind of qualified to talk on this. (Even if you're not from one of those countries, Koreans only use first names with younger people/people they are friends with, so I get where you are coming from.)
I realise that using first names seems weird, but if you are in the UK, I do think that sometimes you have to adapt to some stuff that feels odd and unprofessional. Just as I am far more polite and formal to my mother-in-law than would ever be expected in the UK, I do think that you need to accept that we just call people by their first name, and that no disrespect is meant by it. We show our respect in other ways.
Whenever I have had a boss in Korea who insists on me calling him/her 'Mr Kim' or 'Mrs Lee' while they merrily use my first name without even an honorific attached, it grates on me, because it seems so unfair. I'm not Korean, so I don't even get an honorific, but they get to use an English honorific? It has resulted in a lot of bosses losing respect from westerners I work with.
At my husband's job, they just add honorifics to their first names: so Min Ho Ssi or Min Ho Nim, even for bosses. Things like that are changing in Korea. I don't know what the equivalents are in other languages, but could that be a possibility? That she adds the honorific to your first name?
Forgive me if I have over-stepped the mark, but I have seen both sides. No-one expects you to just disregard your culture completely, but when you are in a different culture, you do have to adapt, even though it seems odd. I didn't think I would ever get used to jumping up to fill my parents in laws glasses with water, or to be expected to listen to my father in law talking without offering any sort of opinion, but I have adapted and it's fine.
The second part - terrible behaviour and I would expect her to get in trouble for that.