It's actually a mashup of (at least) two memes. As mentioned, the name "Brandon" comes from a NASCAR event that spawned the phrase "Let's go Brandon" as a euphemism for "Fuck Joe Biden", so critics began calling Biden "Brandon" in reference.

The "Dark" part came from a series of conservative/MAGA memes from last year, where commenters began to propose that Trump and his allies had been holding themselves back rather than acting as aggressively as they should've, and this vision for the future was called "Dark MAGA", and used a lot of overdramatic anime imagery of Trump as a violent despot serving up the justice his enemies deserved.

"Dark Brandon" emerged as a parody of it, because the idea of Biden as a powerful and ruthless mastermind is, admittedly hilariously absurd.

Reference: Know Your Meme

I believe this sparked the dark brandon name. Originally made by a propagandist cartoonist to make Biden look evil, the left memed it because he's an old man so the juxtaposition is funny, then libs just adopted it as a cool way to brand Biden

That's... a much more bizarre story than I was expecting. Says a lot about the integrity of the MSM too. Oh well. Thanks for explaining!