Honestly I'm sort of in the same situation, and my boyfriend gets weirded out by the name "daddy".
I've just been sort of acting more and more childish around him, like showing him finished coloring in my Hello Kitty book, using my baby voice, and slowly migrating all of my plushies into our bed xD He likes when I act cute, I think it's just the stigma around people thinking it's about relative relations/child involvement. I might tell him one day, but for now I'll be happy with head pats and him not hiding all my stuffies
I haven't gone completely into little space in front of him though ;-;