ATX SMT ALT DEVIATION OVERSHOT DURING CLIMB IN RESPONSE TO WRONG CALL SIGN OR TRAFFIC ADVISORY.

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WE WERE CLRED TO FL370 HDG 185 DEGS AND ADVISED OF TFC AT FL390; WBOUND AT 1100' AND 20 MI. OUT OF 36000' WE HEARD FL390. I THOUGHT WE WERE RECLRED TO FL390; AND RESET THE ALT ALERT SYS TO 39000'; THE RADIO WAS A LITTLE BROKEN. I THOUGHT THE F/O READ BACK TO ATL 'CLB TO 390.' I WAS FLYING SO I STARTED TO CLB OUT OF 37000'. AT 37500' CENTER TOLD US WE HAD 20 SECS TO GET BACK DOWN TO 37000' DUE TO TFC (WHICH I HAD THOUGHT WE WERE CLR OF). THE PROB WAS DUE TO LACK OF COM IN THE COCKPIT; AND A NEW F/O THAT DID NOT UNDERSTAND THE DUTIES OF THE PF AND PNF. WAS A NEW PLT WITH THE COMPANY ON ONLY HIS SECOND FLT. UPON LNDG AT APA I ASKED HIM TO CALL FOR OUR CLRNC TO VNY AND PUT TIMES IN THE CAN. AFTER THE AFTER-LNDG CHKLIST WAS COMPLETE (WE HAD 'HOT CARGO' AND I WAS IN A BIG HURRY) HE GOT VERY UPSET AND SAID FOR ME TO DO IT MYSELF. THIS IS A VERY DEMANDING BUSINESS; AND THE PF AND PNF BOTH HAVE A JOB TO DO; WHICH MUST BE DONE TO HAVE A SAFE FLT. HE WAS GETTING VERY DEFENSIVE AND THREATENED. I WAS NOT TALKING TO HIM AS CAPT AND F/O; BUT AS PF DOING MY JOB AND PNF DOING HIS. HE DID NOT UNDERSTAND THIS. THERE WERE BAD FEELINGS IN THE COCKPIT. I PREVIOUSLY WORKED FOR A COMMUTER AIRLINE WHICH USED COCKPIT RECOURSE MGMNT TRNING OF PF AND PNF WITH OPEN COM IN COCKPIT; BUT CAPT MAKES FINAL DECISION. NO ONE PERSON BEING BETTER THAN THE NEXT--BUT ONE PERSON IS RESPONSIBLE. THE COMPANY I WORK FOR NOW GIVES NO TRNING FOR 2-M CREW'S DUTIES OR RESPONSIBILITIES. I BELIEVE THAT ANY ACFT REQUIRING 2 PLTS SHOULD REQUIRE TRNING IN COCKPIT RESOURCE MGMNT. WHEN IT IS USED RIGHT PF AND PNF; OPEN COM; SAME GOAL SAFE AND LEGAL FLT; USE OF CHKLIST AND MANUALS. THERE IS NO NEED OR REASON FOR ANYTHING ELSE.