Close, but the actual lore is slightly different:
It's true that "Dave" became popular during/partially thanks to a Tevin re-stream, but it's not Tevin who came up with the name. It was actually some random person sending DSP a single cheer with a question or statement that I can't remember, but calling him Dave for no apparant reason at the end of that cheer. DSP reacted in his typical "No idea what you're talking about, dood, but my name is not Dave. Nu-huh. Why is he calling me Dave? I'm not Dave, you've got the wrong person, man, ack ack."-manner.
It became an instant meme and chat kept calling him Dave for the remainder of the stream. Tevin, who was re-streaming said stream, picked up on it, laughed about the randomness of the whole thing and DSP's defensive reaction to it, and kept referring to it as well. And thus the nickname was born, never to go away.
The end.