The drama was meh most of times. I skipped few bits because they were boring. GeunYoung is horribly scatterminded and at some point it's just annoying to watch (especially with her phone, btw horrible plotbunny, writers didn't know any better). Music was ok.
My best guess is that they're using character 霸 Ba4 for her name.
In mandarin if you repeat the main character it gives a cute meaning. She calls herself Baba
Ba4 Ba with the characters 爸爸 means dad