Wow, I think I might’ve had one of those deer girls way back when. They seem vaguely familiar. I had a crap-ton of the mermaids, though! They hung out with my sea ponies.
I cannot guess the name, lol. But I wonder why there are two lines of stitching on the back of her head - one with empty holes and one with the hair, the latter is spaced wider.
It looks like the unused holes might be a hairline that was molded or stamped on to her to act like a guide. I've seen it in some other dolls.
She is an early version of a 70s doll that was an exclusive import from Europe for a department store. They had different natural hair colors and some had tan skin. And her eyes sleep.