I know that she’s known as the 9 day queen but when referencing by name it’s always Lady Jane grey, not Queen Jane or Jane I
I know she could have chosen another name but that’s besides the point
I have heard that it was debated whether she was actually coronated but I’m pretty sure Edward VIII wasn’t and he’s referred to with a royal title.
While you're waiting for an answer...
This is an older, brief, answer from /u/Algernon_Asimov that partially addresses your question:
https://www.reddit.com/r/AskHistorians/comments/uuump/was_lady_jane_grey_technically_a_queen_or_not/
And here are two lengthier answers that address the topic of Lady Jane Gray generally:
/u/intangible-tangerine
/u/RTarcher
https://reddit.com/r/AskHistorians/comments/5k8yt8/what_changed_in_the_political_and_social/dbmk9rm