I assume it's going to be hard enough for the community to know about this fork in the first place, signaling direct continuity is definitely a reason to name the fork so similarly.

Besides, Mozilla has nothing to do with Mosaic, XBMC had nothing to do with Xbox for years...

Incidentally, XBMC has since rebranded as "Kodi" a fee years back.

Seconded. "youtube-dlc" might give an initial brand recognition boost from being similar to "youtube-dl", but it's the community that will make it or break it. Giving it a bad name (as argued by parent comment, and I agree) is not a good start.

I agree. Tho my main intention was backwards compatibility so that changes can easily be merged back into main project. There are also lots of people using it in their python projects. The naming discussion comes up every now and then as an issue. So for now I would like the name youtube-dlc to stay. But depending on how things go in the future I may change the name.

The name makes it seem more like you are attempting a hostile takeover of the project branding. Definitely not a great way to go about this.