Page 18
It's "Luna Naruse", whether you read it from top to bottom or bottom to top!
If anybody is curious, her name is 鳴瀬るな; the 4 characters are read naru-se-ru-na, so if you invert the syllables you get the same naruseruna. Manga is written vertically, which is where the top/bottom comment comes from.
Page 20
I... uh... the rumor... I'm... Luna Naruse, they say...
No idea where that "rumor" bit came from. The "they say" is just wrong. While "<stuff> と言います" (to iimasu) usually means "(somebody) says <stuff>", "<name> と言います" is a standard way of saying what your name is.
So here she was just saying her name with some awkward pauses and an uh/erm (えと) thrown in (i.e. there were no weird words in the middle of the sentence).
Page 22
I have no idea how to interact with girls
I had become a virgin high school girl...!
I think "I have become a cherry boy high school girl" would've been better.
Japanese uses different words for a virgin girl (処女 - shojo; don't confuse with 少女 (shoujo), which just means girl) and a virgin boy (童貞 - doutei). Here she's using doutei and the usual manga stereotype that virgin boys don't know how to talk to girls, which I think also works in English if you use something like "cherry boy".