ACR LGT ALT DEVIATION EXCURSION FROM CLRNC ALT IN RESPONSE TO WRONG CALL SIGN.

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FLT FROM TUCSON TO LAS VEGAS. IN CRUISE FLT AT FL350. I WAS THE PF AND WAS ON AUTOPLT. OUR FLT WAS COMPANY XEE. WE HEARD ATC GIVE AN INSTRUCTION FOR COMPANY EEX TO CROSS 45 NM N OF DRAKE AT FL330. WE (CAPT AND MYSELF) HAD NOT HEARD ANY PREVIOUS INSTRUCTIONS TO A COMPANY EEX AND FELT ATC MAY HAVE MEANT US (COMPANY XEE). THE CAPT CALLED CENTER AND SAID 'UNDERSTAND COMPANY EE TO CROSS 45 N OF DRAKE AT FL330?' ATC ANSWERED AFFIRMATIVE. I BEGAN AN AUTOPLT DSCNT (APPROX 1200 FPM) TO MEET THE RESTRICTION. CAPT AND I THEN HEARD ATC TALKING TO COMPANY EEX. I ASKED THE CAPT TO VERIFY OUR CLRNC TO DSND AND BEGAN A CLB FROM APPROX 34500' BACK TO FL350. THE CAPT GOT A HOLD OF ATC AND CONFIRMED OUR ALT WAS FL350 AND THAT THE DSCNT CLRNC WAS FOR COMPANY EEX. PROB: ATC HAD ISSUED DSCNT TO COMPANY EEX NOT US COMPANY EE; BUT MADE A MISTAKE NOT CATCHING THE PROB WHEN WE READ BACK THE CLRNC. SOLUTION: ALWAYS ADVISE CREWS OF SIMILAR CALL SIGNS AND NUMBERS. BE CAREFUL OF CLRNCS ISSUED TO SIMILAR SOUNDING CALL SIGN ACFT.