No, no, I agree there is something at least suspicious with how he introduces himself:

The three dots are interesting. He started off with a simple sentence, but didn't finish it.
Regarding this comment:
"Or does it feel like something that got handed to you and you just... kept it?"
Maybe it is related to Myrddin not knowing his origins, more specifically, not remembering his past. Like I theorized before, his past and future are nonexistent, like he said himself when he had a breakdown: he has no past (memories) or future (he's stuck in the cube). Maybe he showed up in the cube or was transferred there without much memory, but the Outer or a third party told him his name and that was it. That's why he asks us if his name feels like it belongs to us. And no matter what answer we give to him, there is a strange noise that plays out in that moment (maybe it is a reversed audio? I don't have experience with those, but I don't know if we already have such a thing in the game yet), and then Myrddin just brushes off the comment and continues. Very weird behavior, I wonder if the Voices scared him or pressured him to change the subject or something like that.
And you probably read what I said about his mythological name being related to a mad man who got prophecy powers, so that is very interesting. Currently, it looks like Myrddin is hiding things from us, but I honestly do think parts of his memories are missing since at some points of the story he gets very philosophical regarding why he is in the cube and about himself.
Someone who is simply hiding who they are from us usually wouldn't go as far as creating those minor moments of existential crisis. In summary, I think the name Myrddin is very intentional and has meaning, yes. And he is looking for the meaning of his name, since he doesn't have a "past."
Additionally, I believe a nice way to get into his psyche is to analyze his questions that happen before his future/past breakdown:

Some of those questions show two interesting things, at least initially, to me (and I'm curious to know what you think of them as well):
- Myrddin does not fully know what he is, but he is sure he is not human. We don't know if we are his first interaction with humanity. It doesn't seem likely since in multiple moments he expresses himself as if he has talked to someone else before.
- He probably considered that his past might involve (or he vaguely remembers) him doing something bad, and that's why he is in the box. But he believes (or wants to believe) in second chances or in stopping endless suffering (being stuck forever in the cube).
The last question shown in the screenshot I think is more directed at us, in a way. Like how powerful our words can be and how we can destroy or help Myrddin. Probably related to future endings.
The previous questions, though, they are more intimate:

Like he is testing or exploring our morality, or perhaps ending up leaking his own. I think the questions above show us that Myrddin is trying to fit into something he does not know what it is, and he wants to know if the Player would be willing to give him those chances, eventually. But those questions, I don't think they relate to endings directly, because apparently there are no variables being stored for those, if I recall correctly. (Yes, I just checked again, no variables for those answers.)
Finally, I wanted to mention this sentence he says right before his first breakdown/altercation with the Outer/The Voices in a direct way:

"YOU WILL MAKE IT STOP SOON"
That really stood out to me. What does he mean? Hmm, perhaps he did think ever since the beginning that the player might help him. But do you think he was manipulative since the beginning? I do think he is suspicious, definitely. But perhaps it is early to say with certainty if he is malicious, especially because it does seem like he doesn't want us near the Outer/the Voices, meaning perhaps he does want to protect the player, or at least the connection with the player.
But here is the thing: there is a moment he mentions something crawling in his mouth, something like that. Like it was using his face. I wonder if the Outer/the Voices can pretend to be Myrddin? If they already did it at some point? Interesting and worth keeping in mind.