AN ACR B757-200 CREW FLIES THE MIROK 1 ARR INSTEAD OF THE LYNSY RNAV 2 ARR TO LAS; NV; UNTIL QUESTIONED BY THE APCH CTLR.

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WHILE ON THE MIROK 1 ARR INTO LAS VEGAS; AFTER LEAVING MIROK AWAITING RADAR VECTORS WE WERE ASKED BY APCH TO CONFIRM WE WERE ON THE LYNSY 2 ARR. I REPLIED WE WERE ON THE MIROK 1. WE WERE THEN GIVEN HDG 360 DEGS AND DSCND TO 8000 FT AND HANDED OFF TO THE FINAL CTLR. AFTER LNDG; WE WERE REQUESTED TO CALL THE TRACON. I DISCUSSED THIS WITH THE TRACON AND WAS ASKED IF WE HAD BEEN CLRED VIA THE LYNSY ARR. I REMEMBERED BEING CLRED DIRECT LYNSY BY ZLA BUT NOT THE LYNSY RNAV ARR NOR DID I RECALL READING THAT BACK. THE TRACON INDICATED THEY HAD BEEN HAVING PROBS WITH THE RNAV ARR. UPON REFLECTION AT THE HOTEL I RECALLED THE READBACK BY ME AS CLRED DIRECT LYNSY AND THE ARR. I HEARD THE MIROK ARR BUT DID NOT INCLUDE IT IN MY READBACK. TO PREVENT THIS IN THE FUTURE I RECOMMEND THE FOLLOWING: 1) FULL READBACK OF CLRNCS BY MYSELF. 2) FILE AND CLR US VIA THE RNAV ARRS WITH OUR INITIAL ATC CLRNC (PDC). 3) USE THE PHRASE 'NEW ARR; NOW CLRED' -- SIMILAR TO WHEN FLYING INTO LAX -- ALLOWING TIME TO SET UP THE NEW ARR (IE; MITTS VERSUS CIVET). 4) NAME ARRS SO THEY ARE NOT EASILY CONFUSED. BOTH LYNSY AND MIROK ARE ON BOTH ARRS. NAME THE RNAV ARR WITH A DISTINCTIVE INTXN ONLY APPLICABLE TO ITSELF SUCH AS UTARE; WHICH IS ONLY ON THE LYNSY RNAV 2. 5) DELAY PUTTING THE ARR INTO THE FMC. OUR INITIAL ATC CLRNC AT DFW INCLUDED THE MIROK 1 AND WE HAD THAT IN OUR PLANS AND LOADED IN THE FMC. 6) THIS FLT WAS AFTER AN ALL NIGHTER TO MIA -- SLEEP DURING THE DAY AND 2 LEGS MIA-DFW-LAS. DESPITE OUR SLEEP PLANNING; FATIGUE PLAYED A ROLE.