In-game History:The original game was called "UFO: Enemy Unknown" and the organization was called XCom or XCOM (standing for "eXtraterrestrial Combat unit") in all manual and in-game references.
Following the success and franchising of the series, the organization became X-Com or X-COM in all the following game names, manual and in-game references, starting with "X-COM: Terror from the Deep" and the American re-release of the original as "X-COM: UFO Defense".
With Take-Two/2K's new series, the game names and organization went back to just being XCOM.
Trademark History:XCOM TERROR FROM THE DEEP (March 7, 1995; Microprose)
X-COM (May 25, 1995; Microprose)
X-COM UFO DEFENSE (May 25, 1995; Microprose)
X-COM APOCALYPSE (July 3, 1997; Microprose)
X-COM INTERCEPTOR (March 19, 1998; Hasbro)
X-COM ALLIANCE (September 29, 1998; Hasbro)
X-COM (May 7, 2007; Take-Two)
THE BUREAU: XCOM DECLASSIFIED (June 7, 2013; Take-Two)
XCOM ENEMY UNKNOWN (July 11, 2013; Take-Two)
Final Conclusion:...yes.