If it's your software send a DMCA. They have a legally required timeframe to process those. If it's open source, however, then you don't have any valid DMCA claim.
Open source code is still copyrighted. What the license defines is rights that people have in distributing that code. If an unofficial repository is using open source code to ship malware, and the license that software had didn’t allow that, then the unofficial repository is still breaking copyright law despite the code being open source.
It's not illegal to send an incorrect one by mistake but GitHub probably won't process it. It's illegal to send an incorrect one intentionally. Now that it's been pointed out to you that making malware isn't a copyright violation, it's intentional if you send a DMCA anyway.
Now, projects might choose to license their logo permissively, but that's an active choice.
EDIT: e.g. https://www.mozilla.org/en-US/foundation/trademarks/policy/
You're correct I was overly broad about the actual name use being DMCA-able though.