The name search might be settling in on Fred, short for Winnifred from Once Upon A Mattress. The song "I've always been shy" particularly resonates, as does lung power reminiscent of the young Carol Burnett in the role. Choruses of "I'm in love with a girl named Fred" are also appropriate.
There were brief mentions of calling her Squirrel for her magnificent tail, but Squirrel is a little difficult to pronounce. I did want to name her Ista, but the pronunciation again stopped me--that first syllable kept coming out like a hiss. Suggestions by the nieces to riff off Fish were also rejected. (No, we're not calling her Chips. Or Shark Bait.) Nephew's suggestion of Suzie after a classmate was also rejected. So we're giving Fred a test run, and unless some other name manifests itself, Fred will probably stick.