From what I recall, Tigers, Saints, Wasps and Harlequins names go way back to the 19th century, in the very early years of the clubs, and have non-commercial origins. Those ones seem fine to me.
IIRC Tigers had links with the local regiment who were nicknamed the "tigers".
Saints were set up by a priest, and named after his church.
Harlequins and Wasps were set up when another club split into association football and 2 rugby football clubs. Was it Hampstead? The rugby members agreed to meet at a pub and thrash out the details but wanted to keep the initials, flicked through a dictionary under "H" and thought "Harlequins" sounded fun. Other rugby members went to the wrong pub, and got drunk instead of trying to find the right one, and ultimately set up Wasps - I've no idea why.
All the others, like Chiefs, Shoguns, Bears, Bees etc were all marketing gimmicks to appeal to new young fans who might support a team because its name rather than its play or location (I gather this is an actual thing over the pond - and I guess people often pick horses that way for the Grand National etc). It's always been tacky and cheesey.