Mercedes make cars. and engines
Mercedes supply engines to Mclaren (who incidentally also produce their own
cars) and due to the intricacies of contracts/prior relationships/
past projects, Mercedes get to have their name registered as part of the team name which presumably makes for good advertising. This doesn't happen with Force India to whom Mercedes also supply engines. I do not know why.
Not content with getting their name and logo all over Mclaren's F1 cars, Mercedes also decided to buy out Ross Brawn's old team Brawn Racing (who themselves only a year prior were owned and named after Honda) in 2009 and rebadge the entire team as Mercedes or Mercedes Petronas (after their chief sponsor) as putting their engine supplier after their name would leave them with Mercedes-Mercedes which sounds fucking stupid.
Ferrari also have their own team (called Ferrari) yet also supply engines to Sauber who don't call themselves Sauber Ferrari. I have no idea why Ferrari haven't gone down the free advertising route by insisting on naming rights but then italians have always been a little bit tricky like that.
Anyway by having their own F1 team, Mercedes can get to hear Germany's national anthem 'Deutschland Uber Alles'* played after the driver's national anthem whenever they win a race unlike when Mclaren win and they are forced to listen to 'God Save The Queen' instead. Either way, at least it's meant that Red Bull haven't won so we are spared the suicidal dirge that is the Austrian national anthem**.
*not that we don't get to hear it enough already
** not that the team are based in bloody Austria either. Pretty much every team bar Ferrari, Sauber and Torro Rosso are ultimately British. Oh and Red Bull is originally a bloody Thai drink too!