We watched it last night. Not great, not terrible. Definitely trying to be a "fun" show - much more "Adventures of Lois and Clark" than Arrow or Gotham.
I'll give it a few more tries to see if it gets better now that the set-up pilot stuff is out of the way.
I'm also bothered that they chose "Kara Danvers" as her name. I'm not a big DC guy, but I believe it's supposed to be Linda Lee Danvers or Kara Zor-El.
Kara Zor-El is her true name. Kara Danvers is her secret/earth identity name. Yeah, comic Supergirl used Linda Danvers but I can understand simplifying that for TV and keeping the first name the same.
They even go so far as to call Kara "Agent Danvers" in one of the trailers, when Carol Danvers from marvel is referred to as "Agent Danvers" from SHIELD. I call Shenanigans!
"Agent Danvers" on the show is actually Kara's adoptive sister Alex Danvers. She works for the DEO, which is very much a DCU-style version of SHIELD.
And of course there are shenanigans. There have been for years and years between DC and Marvel. Of course DC is trying to cash in on the groundwork laid by Marvel movies.
Are they similar in name? Sure, but that street goes both ways. It's entirely possible that Marvel chose the last name "Danvers" for their new blond super-heroine in the late 60s because they were trying to copy Supergirl.