All you have to know about Ringo’s drumming is what other professional drummers say about him. He’s held in extremely high regard.
Excellent pocket/groove drummer, just not a flash jazz-fusion drummer (thank god), which was what was coming into vogue by the end of the ‘60’s. Also very versatile, having no issue with keeping up with the growing complexity of L & M’s writing and the overall production of the music. Oddball time signatures…shifting time signatures within a song…Harrison’s Eastern-influenced stuff…McCartney’s vaudeville stuff…he handled it just fine.
My personal favorite performance of his is the drumming on Rain - that’s a very active drum part, and it’s even more impressive when you realize the backing was recorded roughly half again as fast, then the tape slowed down for the final mix. Mr. Starkey was cooking on that track.
As much as anything, a good indication of his ability is that on a whole lot of Beatle songs, if you listen just to the drum track, you can tell the song. He had some wonderfully idiosyncratic parts. Very supple playing style.
Oh…as to the name “Beatles,” that evolved over time, but was first thought up as an homage to Buddy Holly & the Crickets, by Stu Sutcliffe (if the part of my brain dedicated to Beatles lore isn’t malfunctioning). Spelling changed a few times before settling on Beatles-with-an-A, and yes, due to playing “beat” music.
Oh, and remember when it became trendy for rock stars to put out albums of pop standards from before the rock era (looking at you, Rod Stewart…
)? - Ringo did it first, all the way back in 1970 with his first solo album, Sentimental Journey, anticipating the trend. That’s just a weird little bonus.