Hozier is the name of the guy and he has a back-up band (I don't know if it has a steady line-up), "Hozier" is not like "Bon Jovi", the media don't say "the band called Hozier" but "Hozier, the singer songwriter".

I loved his gig at Coachella (idk if it's online, I watched the live streaming during the festival) and I love his duet with Annie Lennox (but I love Annie so I'm biased!). He's got a powerful soul voice, clever lyrics and good music to go with. It's very refreshing to see that there's still a place for talented artists who are different from the mainstream prefab/manufactured music heard on the radio/TV.

https://youtu.be/HZEChv1AaOk