I just got my PS4 a few days ago and went onto my PSN account that I had back when I had my PS3. 

I did the whole real name thing and entered it, but now I would like to remove it because everytime in my activity feed it says "[Real name] has done this, [real name] has done that, etc, etc."

It also says it right when I go to my PSN profile right on top of my actual PSN gamertag. I don't care about who knows my real name, I just don't want to get referred to as it. I have a PSN ID for a reason. 

Is there any way to change this?

The default privacy setting makes it so they only see your RN when you or they request it.

So does everyone have their real name on top of their PSN ID on their profiles? And if so does that mean other people viewing their profiles only see their PSN ID until they request real name? 

If so I don't mind that.

I'm just confused because I think I remembered choosing "anyone can see" or something like that when the real name option popped up, but I don't remember.

Double check your privacy setting,  but they should only see it upon you two mutually agreeing to share RN

Yeah I double checked plent of times but there is no clear option, and there's also no way to just remove real names completely.

I don't wanna sound like i'm making a big deal out of nothing, because if it's something I can't change then oh well, but if I had the option I would like to.

I just don't want people to see me online as my real name, because I have a PSN ID that I like and chose for a reason. 

I feel and hope that what you said is right though so thanks for the help bruh. 

My real name on PSN is Viv Ster. Problem solved.