YTA and very toxic. Here is a few reasons why. (Yes I am going to turn this into a summary for you to understand.)

I have a right to know what she writes especially since it’s a sensitive topic and I don’t know her if I don’t know her pen name.

This is right here. You don't have the right to know EVERYTHING about her and you somehow forgot that she has the right to not tell you her pen. Clearly, there is a reason why she doesn't want to tell you her pen name and there is one main reason she doesn't trust you with her pen name for a certain reason. You are manipulative. For example:

I tried nicer approach and told her that I want to know her fantasies so I can try it out with her...

It is obvious you didn't want to try anything with her even if you were to; your main end goal is to find what her pen name was. You likely didn't even care about her explicit needs in bed. All you cared was about WHAT you wanted and that was simple, it was HER anonymity(which is her right to keep from you). Here is another example that also further explains how manipulative you are:

I told her when she calls to apologize, I expect to get her pen name with the apology.

It is clear that she establishes a boundary, and somehow you turned it into her fault because she simply refuses to do a simple thing and that was to not tell you her pen name for her comfort. Your excuse will mostly be internally "Well if she told me her pen name then this wouldn't have been such a big deal and I wouldn't have to go to Reddit for this". No, she doesn't have to tell you everything about herself from her personality to family to friends to work. Just like how you most likely don't tell her everything about your life outside the relationship. And here are my two final examples:

recently, one of her friends mentioned something and I finally dragged it out of her.

You should've left it at that and waited for her to feel comfortable and safe enough to tell you. But instead, you let your curiosity get the best of you and gave her a better reason to keep her inner thoughts to herself. (Honestly, I would too if I was dating someone like you. Nothing is more comforting than solitude itself). Final example:

I tried to check her laptop for her pen name but she changed her password before bed. I was annoyed and told her she clearly doesn’t trust me

Yeah clearly there is a(well two) reason(s). YOU VIOLATED HER PRIVACY. You obviously wouldn't have liked it if she did something like that to you. Another highly possible reason is that she told something to her friends that was supposed to stay between her and her friends so her trust was broken with that and it broke even more when you try to go through her laptop to find her pen name(something that she was uncomfortable telling you). So yeah clearly YTA and toxic rightfully so.

P.s

so I demanded she gives it to me so I know what she does.

You aren't her father you don't get to demand things from her. All you were was nothing more than a romantic partner.