<Geek mode on> The name is an homage to the RB211 series of engines, the first triple-spool jet engines. Obviously there’s a connection with RR amongst the workforce.
Superb engine, however its protracted development (the first stage compressor blades were originally carbon and couldn’t cope with the forces involved which led to the single crystal Titanium blade) led to RR needing a government bailout and Lockheed nearly going under too as the engine was the sole option for the L-1011 TriStar being developed at that time (superb aircraft!) . Not having used any other make of Turbofan, I believe the RB211/Trent has a weight penalty over its competitors, but has better reliability and spool-up time.
It’s still in use today as an engine for gas-pumping uses as it’s so reliable and the Trent engines on B777, 787 and A330/340/350/380 aircraft are based on the RB211. <Geek mode off>