I think definitely!
I live in the US and I am a [name_f]Margaret[/name_f] who is just [name_f]Margaret[/name_f]. When I was little I went through a phase where I decided that I was just [name_f]Greta[/name_f], and no one was allowed to call me [name_f]Margaret[/name_f]. Now, I’m just [name_f]Margaret[/name_f].
Throughout high school teachers would always ask me if I had a nickname. I always told them no, just [name_f]Margaret[/name_f]. There were a few (mostly my freshman year) who called me [name_f]Maggie[/name_f] or [name_f]Mags[/name_f] anyway and I never corrected them cuz it was too much of a hassle. But it was restricted to those few teachers and I never got nicknamed by anyone else. In short, [name_f]Dorothy[/name_f] can definitely be just [name_f]Dorothy[/name_f]. There are some people who might nickname her anyway, and she might choose to go by a nickname, but it is totally possible for her to be just [name_f]Dorothy[/name_f]!