POTENTIAL CONFLICT AND POSSIBLE CFTT IN AN ALTDEV.

Narrative

WE WERE AN LGT X; DEPARTING SLC TO DENVER VIA DIRECT SLC VOR; J-56 DEN. COMPANY LGT Z DEPARTED BEFORE US. COMPANY LGT Y DEPARTED AFTER US. EACH OF US HAD THE SAME RTE -- SLC; J-56 DEN; AND ALL TOOK OFF FROM RWY 16R. AFTER TKOF AND CLRED TO 8000 FT; WE WERE TURNED TO 280 DEGS AND TO MAINTAIN VISUAL SEPARATION ON LGT Z. SWITCHED TO SLC DEP WE WERE INSTRUCTED TO CLB TO 9000 FT AND FLY 300 DEGS. MEANWHILE; LGT Z WAS CLRED TO THE SLC VOR FLT PLAN RTE AND CLRED TO 16000 FT. WE WERE TURNED TO 330 DEGS AND TOLD TO STAY AT 9000 FT DUE TO LGT Z XING OVERHEAD. MEANWHILE LGT Y CHKED IN AND RECEIVED SIMILAR VECTORS. WE WERE CLRED DIRECT SLC VOR FLT PLAN RTE WITH NO ALT CHANGE. LGT Y WAS CLRED TO 16000 FT; WHICH THEY ACKNOWLEDGED. WE COULD SEE THE ARRIVING ACFT AT 9000 FT IN THE 16R TFC PATTERN AND SAW A POTENTIAL CONFLICT BUT WE WERE STILL 5-6 MI FROM THE NEAREST ACFT. OUR TCASII WAS WORKING OK AND SHOWED THE OTHER ACFT. SLC DEP CALLED (SORT OF FRANTICALLY) AND TOLD US TO EXPEDITE OUT OF 10000 FT. WE TOLD HIM WE HAD NEVER BEEN CLRED OUT OF 9000 FT. HE SAID HE HAD CLRED US TO 16000 FT AND MAYBE LGT Y HAD ANSWERED. LGT Y THEN STATED THERE WAS ONLY ONE 16000 CLB AND IT HAD BEEN FOR LGT Y. WE CONCURRED. WE IMMEDIATELY CLBED OUT OF 9000 FT TO 16000 FT. THERE WERE NO NEAR MISSES; JUST CTLR CONFUSION WITH 3 CONSECUTIVE DEPS WITH SAME RTING AND 2 VERY SIMILAR CALL SIGNS. AFTER IT WAS OVER THE CTLR ADMITTED HE WAS CONFUSED WITH THE SIMILAR CALL SIGNS. AUTOMATION INFO: I TURNED THE AUTOPLT ON AFTER THE INITIAL LEVEL OFF AT 8000 FT (BEFORE THE CONFUSION) SO THAT WE WOULD HAVE BETTER SITUATIONAL AWARENESS. UNFORTUNATELY THE CTLR DID NOT HAVE THE SAME CAPABILITY.