B737 FLC INADVERTENTLY TOOK OFF PRIOR TO TKOF CLRNC DUE TO MISTAKING THE RWY NUMBER WITH THEIR CALL SIGN NUMBER; WHICH WAS THE SAME.

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AFTER PUSHBACK; WE WERE CLRED TO TAXI TO RWY 12R AT HOU ARPT. THE ARPT WAS IN THE MIDST OF CHANGING ACTIVE RWYS AND AS A RESULT; SEVERAL RWYS WERE BEING USED. WE WERE INSTRUCTED TO 'HOLD SHORT OF RWY 12R' AND WE SWITCHED OVER TO TWR. TWR WAS VERY BUSY AS HE HAD 2 OPPOSITE DIRECTION DEPS (RWY 30L) WAITING FOR DEP; ANOTHER ACFT WAITING FOR TKOF AT RWY 22 AND US (ACR X); HOLDING SHORT OF RWY 12R. IN ADDITION; HE WAS HANDLING AN FAA FLT CHK ACFT FLYING AN APCH TO RWY 12R (ILS). BOTH THE CAPT AND I HEARD OUR CLRNC 'ACR X CLRED FOR TKOF; TURN L HDG 150 DEGS.' I BEGAN THE READBACK BUT WAS CONFUSED AS TO THE TURN. (A 150 DEG HDG FROM RWY 12R IS A R TURN.) I FUMBLED AND THEN READ BACK 'HDG 150 DEGS; CLRED FOR TKOF; ACR X.' ON ROLLOUT; I REMEMBERED HEARING TWR URGE AN ACFT ON RWY 22 TO BEGIN HIS ROLL. THAT ACFT INDICATED WITH SOME CONFUSION THAT THEY HAD NOT ACCEPTED A TKOF CLRNC AND THAT THEY WOULD NEED ADDITIONAL TIME ON CLBOUT. WE THEN WERE TOLD BY TWR 'ACR X CLRED FOR TKOF; TURN L HDG 350 DEGS.' WE QUERIED TWR AND AGAIN RECEIVED THE SAME CLRNC. WE HELD OUR HDG OF 150 DEGS AND EXPLAINED AGAIN. TWR TOLD US TO TURN L TO A 350 DEG HDG AND HANDED US TO DEP. I BELIEVE WE WERE CONFUSED WITH THE ACFT AT RWY 22 BECAUSE OF OUR CALL SIGN. I ALSO BELIEVE THAT SEVERAL DISTRS AT THE TIME CAUSED THE CTLR AND US TO FAIL TO CATCH THE MISTAKE.