Soldiers generally know more history than you expect. If they used Geronimo it's likely a top o' the hat to the warrior, not a call back to a hokey movie.

Especially because real soldiers never cry 'Geronimo' when they fall out of airplanes - they're counting the seconds until the chute deploys.

Also - the army especially has taken the Indian warrior thing to heart: helicopters are named after tribes, call signs and etc.