Sunflower is a nice girl's name... and is the state highpoint of Kansas.

You could name her after a style of climbing you enjoy, though names like "Crack", "Handjam", "Fingerlock", "Smear" or "Off width" might get a certain amount of teasing in grade school. "Free" on the other hand is not a bad name for a girl, though a bit reminiscent of the 60s.

Katahdin (Kate).

Name her Elie after Elie De Beaumont.

Lizard Head?

Sugarloaf!

I named my female cat Denali. She is the great one

Name her K2. Every guys greatest challenge

What about Bonney? Whatever you do, don't name her after Mt Hooker unless you want a visit from social services.

maybe Anna. Sort of short for Annapurna

I can't believe no one has said Montana!

Personally I like some of the other Spanish words for mountains, like Sierra and Nevada, overdone as they may be.

I'm thinking of crazy words from our lexicon like Arete and Cirque...

and if you want to keep guys away from her....

Bergshrund!

Siula? Maybe Elia after Mt. Saint Elias...