Thank you all for some wonderful suggestions! I saw so many new things in the lace motif after reading all of the comments: umbrellas, cathedral windows, flying birds-- what fun! The fact that I've decided to stick with the name "Carlotta" is more a reflection of how I've come to think of the pattern, and the memories I have of a day spent at Villa Carlotta, than a choice based on the merits of each suggested name.
So I've decided to give two free patterns away: one to Jeanie, because I thought the name Azalee was especially beautiful, and one to Aimee, because after reading her comment, I could actually see the sandhill cranes in flight across the top of the beret (all on a collision course towards the center, but that's neither here nor there!). I've finished the chart for the hat, but I'm thinking I will write out the directions as well-- I encourage the use of charts (and prefer them myself), but I realize that some knitters would rather follow written-out instructions. So I would guess that the pattern will be finished within a week or two, and I will email it to the winners as soon as it's ready.