Just to clear up a point, Lee was her chosen family name. Supergirl used her super-hearing to listen in on many Earth girl names and chose the name "Linda Lee" for herself when she registered at the Midvale Orphanage. This followed the LL naming convention in Superman mythology. When she was adopted by the Danvers, then her full name was Linda Lee Danvers, but she was usually just called Linda Danvers.
Maybe Supergirl was being coy and keeping her house name--El--in her name, in a round about way. And I imagine Otto Binder was thinking of the young singer Brenda Lee who was rising in popularity at the time.
It's probably not right to develop a crush on a paper character in two-dimensions, but I think I had a crush on Linda Danvers when I discovered her at the age of 8, in the back pages of ACTION COMICS. I had blonde hair, but I guess the brown hair and the headband did something for me. She looked just like a lot of older girls that would hang around with my sisters. And I've posted before that she reminded me of Shelley Fabares on THE DONNA REED SHOW.
There was a distinct difference between Linda and Supergirl--so hers seemed an effective disguise.
The interesting thing with the TV Supergirl is that up until recently, Melissa Benoist's hair always looks a bit browner as Kara Danvers than as Supergirl, where her blonde highlights seem more prominent. It could be a trick of the light or I might be seeing something that isn't there.
However, in the last few episodes before the break, Benoist's hair looked much blonder in both identities.