AN MD80 CREW; DEPARTING MMMX; WERE QUERIED BY ATC WHEN THEIR TURN; AT THE 5 PT 5 DME FIX WAS A R TURN INSTEAD OF A L TURN.

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20 MINS PRIOR TO TKOF; I INFORMED THE CAPT I WAS GETTING OUR CLRNC FOR OUR RETURN LEG TO DFW FROM MEX. I WROTE THE CLRNC ON A PIECE OF PAPER AS UJ81 NLD AS F MAINTAIN 350 VIA TOLUCA A1 SQUAWK XXXX. I THEN PULLED OUT THE DEP AND COMMENTED TO THE CAPT 'THIS IS STRANGE; THEY HAVE US MAKING A R TURN AFTER TKOF; WE ALWAYS MAKE A L TURN AT VASOS INTXN.' HE SAID 'CALL THEM BACK TO VERIFY.' SO I CALLED CLRNC DELIVERY AND ASKED 'VERIFY IT IS THE TOLUCA ALPHA 1 DEP FOR ACR X.' THEY RESPONDED 'AFFIRMATIVE.' THE CAPT WAS FLYING AND UPON REACHING VASOS; HE INITIATED A R TURN TO INTERCEPT THE 197 DEG RADIAL AND DEP ASKED WHAT OUR HDG WAS. I TOLD THEM 'WE ARE IN THE R TURN TO 197 DEGS.' DEP ADVISED US 'THAT WAS NOT YOUR CLRNC; TURN L TO A HDG OF 350 DEGS.' I HAD THE TERRAIN FEATURE ON MY SIDE AND STILL THOUGHT IT WAS ODD THEY GAVE US THE TOLUCA ALPHA 1. THE TERRAIN WAS NEVER A PROB -- IT WAS IN SIGHT VISUALLY AND THROUGH THE GPWS. DEP THEN ADVISED US THAT WE WERE GIVEN THE TULAS ALPHA 1 DEP. I TOLD THEM I HAD CALLED TWICE TO VERIFY THE CLRNC. I NOW SEE WHERE THE PROB LIES: THE 2 DEPS SOUND THE SAME. THEY CAN BE EASILY CONFUSED. PLEASE CHANGE THE NAMES OF THE DEPS TO SOMETHING OBVIOUSLY DIFFERENT FROM ONE ANOTHER. SUPPLEMENTAL INFO FROM ACN 545196: AFTER RECEIVING CLRNC FROM MEX CLRNC DELIVERY; MY FO TOLD ME THAT OUR DEP WAS NOT WHAT WAS ON OUR FLT PLAN. THE FLT PLAN HAD TULAS ALPHA 1 -- ATC GAVE US TOLUCA ALPHA 1. I HAD THE FO VERIFY 2 TIMES OUR DEP CLRNC. BOTH TIMES IT WAS READ BACK TO ATC AS TOLUCA ALPHA 1. UPON DEP; AS WE TURNED R AS THE TOLUCA ALPHA 1 DEP READS; WE WERE TOLD THAT WE WERE IN ERROR.