>>I wonder if it will always be called RapGenius for non-rap content, or if they'll come up with a more general brand name

They appear to have decided to keep it all on the rapgenius.com domain but are calling the different verticals "_____ Genius"

If you hover over 'rap' in the navbar you see a dropdown with the following:

-rock -> links to rock.rapgenius.com

-poetry -> links to poetry.rapgenius.com

-news -> links to news.rapgenius.com

On those subdomains the logo reads 'rock genius' 'poetry genius' or 'news genius'. I checked and they own the .com for each of those as well, which redirect to the subdomains. They also have corresponding Facebook and Twitter accounts.

Tech Genius next please!