A B737-300 DEPARTED ZZZ AFTER #1 REVERSER WAS DEFERRED PER THE MEL BUT THE CREW DID NOT ADVISE DISPATCH OF THE DEFERRAL.

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WE WERE FLT XXXX/XXX ZZZ-ORD. UPON INITIAL PUSHBACK; WE EXPERIENCED A REV UNLOCK LIGHT ON #1 ENG. THROUGH ZZZ OPS; A PHONE PATCH WAS MADE WITH MAINT. BEING TOWED BACK TO THE GATE AFTER TROUBLESHOOTING; OPS WAS TRYING TO LOCATE CONTRACT MAINT ON FIELD TO TROUBLESHOOT AND DEFER. DURING THIS TIME; CAPT WAS IN OPS AND I REMAINED ON BOARD. I RECEIVED FROM DISPATCH TO EXPECT RELEASE 2 PER THRUST REV AS PER MAINT. I RECEIVED RELEASE 2; BUT WITH A NEW RADIO CALL SIGN. AFTER MAINT DEFERRED THE #1 THRUST REVERSER; I COORDINATED WITH CLRNC TO VERIFY OUR NEW CALL SIGN AND VIA ACARS RELEASE VERIFICATION 2. ALL WAS ACCOMPLISHED SOP. AFTER TKOF; DISPATCH WANT TO VERIFY ACCEPTANCE OF #1 THRUST REVERSER DEFERRED. CAPT AND I FORGOT TO LET DISPATCH KNOW ABOUT DEFERRAL PRIOR TO TOW; AFTER WE RECEIVED THE MSG FROM DISPATCH. CAPT AFFIRMED THAT THE #1 THRUST REVERSER HAS BEEN DEFERRED. WE TALKED ABOUT IT. WE WROTE IT ON THE ACARS; PRINTED RELEASE #2 WITH ZULU TIME AND ATTACHED DISPATCH MSG TO THAT RELEASE. WE BOTH HAD SAFETY OF OUR PAX ON THE FOREFRONT OF OUR MINDS; BUT WE FORGOT TO KEEP DISPATCH IN THE LOOP BY LETTING THEM KNOW THAT THE #1 THRUST REVERSER HAS ACTUALLY BEEN DEFERRED. DISPATCH KNEW MAINT WAS WORKING ON THE PROB; BUT DID NOT KNOW IT WAS FINISHED. CAPT AND I TALKED ABOUT IT AND HOW HE WENT OUT OF HIS HABIT PATTERN AND I ACKNOWLEDGED THAT MY PART WAS NOT DONE EITHER BY INQUIRING IF DISPATCH HAS BEEN CONTACTED.