What's it called when you want to write fanfiction, but won't say the character's name or the fandom?

This is maybe the second time I did this. Its when you have an idea for a story with a specific character in mind, but for some reason you dont want anyone to know who that character is. I don't know maybe out of shame, of liking the character or the fandom. 

But i would write a story, about a specific character in mind, but wont say their actual name. Im only hinting its them, by personality and vague physical characteristics, like hair color. If they have a very recognizable physical trait, then I wont say it. Its like I want to write about that character but i want it to be vague, so people wont realize who it is. Its a type of story that makes you think "This reminds me of a character" and it happend because the story was exactly about that character. 

Idk, I wonder if this thing has a name. And if its ok to do this, or get over the fear of being cringe and write the actual names. Because I feel bad in a way, because I know its not a character created by me, but its written in a way that people might think it is. 

I don't know, what do you think I should do?