…or is it a TV trope?
Question inspired by South Park’s Timmy and Game of Thrones’ Hodor, but since there ought to be a straight yes/no answer I think it belongs in GQ, not CS.
I’m aware that there are people with very limited vocabs, and people with no vocabulary at all. What I’m asking is whether there are people whose vocab is limited entirely to their own names.
Leaffan
Hodor wasn’t his original name. It’s just all he said, so they started calling him Hodor. This is from the books. So spoiler alert, or whatever.
The end of a post is a great place for a spoiler alert. 
Yes, aphasia affects many people following a stroke and other forms of brain damage. People may be limited to a small set of words. I know someone who is limited to the words ‘no’, ‘shit’, and ‘more’. He can still communicate fairly well through grunts and gesticulation.
Garp.
Pika-pika-pikachu! (I have a grandson.)
Feck!!!
Drink!!!
Arse!!!
This response actually works really well with the username 
Timmy can say what sounds like “living a lie.” And IIRC one time he said “…and the Lords of the Underworld.”
And that sounds like Yarp! (The guy from Hot Fuzz. Although his name is Michael Armstrong. Played by, yarp, Sandor Clegane.
Factually: there is a famous aphasia patient who was nicknamed “Tan,” after the only/main thing he could say. He got it from brain damage, though, and his name was maybe Leborgne.
I think you mean LEAFFAAANNN!!!
Autistics(even those who are otherwise non-verbal) can sometimes have a word they repeat a LOT, it can be their name or a name or any other random word or phrase. I’ve read on blogs where parents will puzzle over the origin or meaning of their child’s word or phrase. I believe it is called echolalia or verbal stimming.
http://lessonplans.blogs.nytimes.com/2008/10/15/it-bears-repeating/?_r=0
Thinking back to when I worked with special needs kids, there is one who I can remember saying only his own name. This is a memory that’s around ten years old, though, so there could have been another word of two he said that I’m not remembering.
Regardless, he didn’t say his name with the frequency that Timmy does. Nor was he as functional.
“Shit!”
"Fuck.’
“Who the hell wrote this script?”
Also from the DVD (in the extra features, at least). His name is Walder, or something like that.
Malkovich Malkovich! Malkovich?* Malkovich!!*
Marklars can Marklar Marklar Marklars, but Marklar Marklars Marklar.
Before I started school there was a kid in my neighborhood who never said anything except for “Sy Fry.” So that’s what we called him. It was okay with everybody, I guess, because we all hung around together and he wasn’t left out.
They moved away before we started school so I never found out if he ever finally did say anything else.
Are you out there Sy Fry?
I was just complaining about this exact topic to my friend! I work in special education, with a wide range of kids, and I have never met a single one who could only say his own name. Plenty of nonverbal kids, plenty of kids who can say only a few words, plenty of kids who make repetitive nonsense vocalizations, but no kids who just say “Timmy!” In fact, in my experience, the more severely impaired a child, the less likely they are to know or respond to their own name.
Well, looks like the answer is that it’s a trope, not reality.