Text taken from the petition site:
SpaceX has been awarded the contract to produce NASA’s next manned spacecraft, which is tentatively scheduled for launch in 2015. We’re calling on SpaceX founder and CEO Elon Musk to christen the first of these manned Dragon capsules “Serenity,” after the fictional ship of the same name in Joss Whedon’s “Firefly” universe.

Tell SpaceX: Next manned US spacecraft should be named “Serenity”

We respectfully encourage SpaceX to christen the first of their manned Dragon spacecraft Serenity, after the ship of the same name in Joss Whedon’s “Firefly” universe.

A Dragon spacecraft with this name would represent the shared hopes and dreams of everyone who is cheering for the success of an American space program that has been revitalized and revolutionized with the help of private industry–people who, like the diverse crew that shares a common goal in Whedon’s Serenity, envision a world where a privately-owned spaceship represents the opportunity for a better life and the spirit of independence can be realized in space.

Christening the first Dragon in honor of Whedon’s fictional spaceship would not only speak to the important role that man’s ability to dream without constraint plays in providing the spark that fuels the fire of human achievement, but as the first manned spacecraft built by a private entity, it would also represent the hope of a future in which the blessings and true freedom that only the stars can offer will be open to every man, woman and child. We believe very strongly that there is no name that would reflect this better than Serenity, and we urge you to give the name your serious consideration.

Thank you.