By Irene Klotz

CAPE CANAVERAL, Fla., April 13 (Reuters) - Hours after unveiling its next-generation "Vulcan" rocket, the company that launches most of America's satellites, United Launch Alliance, ran into its first problem - the rocket's name.

"Vulcan is a trademark of Vulcan Inc. and we have informed ULA of our trademark rights," Chuck Beames, president of the Paul Allen-backed Vulcan Aerospace told Reuters.

"Paul Allen and Vulcan were early leaders within space exploration with the launch of SpaceShipOne more than a decade ago. We are flattered by ULA's tribute to our legacy by naming their new rocket 'Vulcan,'" Beames added.

ULA, a joint venture of Lockheed Martin Corp and Boeing Co, selected Vulcan as the name of its new booster, which will be developed in phases beginning in 2019, after it won more than 1 million votes in a crowdsourcing initiative.

On Monday, ULA unveiled the reusable "Vulcan" rocket that is slated to end U.S. dependence on Russian-built rocket engines.

During a webcast news conference, ULA Chief Executive Tory Bruno playfully tossed away baseball caps bearing the names of finalist names, including "Galaxy One" and "Zeus."

"This is a collector's item now," he quipped.

The flaming logo of the Vulcan rocket may not be far behind.

ULA did not immediately respond to a request for comment about Allen's trademark challenge.

(Editing by Ken Wills)