ONE CITATION JET FLT CREW AND THE TRAINEE TEB GND CTLR CONFUSED CALL SIGNS WHICH CAUSED A RWY INCURSION AT TEB.

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MYSELF AND AN FO WERE DEPARTING FBO AT TEB FOR RWY 1. OUR INITIAL CLRNC WAS TO TAXI ON TXWY L AND HOLD SHORT OF RWY 6 BEHIND THE ASTRA JET. RWY 6 WAS IN USE FOR LNDG. THERE WAS ANOTHER JET; ACFT Y; ON THE FIELD TAXIING OUT TO THE DEP RWY. ACFT Y WAS HOLDING SHORT OF RWY 6 ON TXWY G AT THIS TIME. FOR SOME REASON ACFT Y KEPT ANSWERING TO OUR CALL SIGN. THE TWR THEN CLRED THE ASTRA JET HOLDING SHORT OF RWY 6 ON TXWY L TO CROSS AND CLRED US TO FOLLOW THE ASTRA JET ACROSS THE RWY. AT THAT TIME ACFT Y ANSWERED AS ACFT X. SHORTLY AFTER; WE ALSO ANSWERED OUR OWN CALL SIGN. ACFT X CROSSED RWY 6 ON TXWY L. ACFT Y ALSO CROSSED RWY 6 ON TXWY G. TO FURTHER COMPLICATE MATTERS; THERE WAS AN ACFT ON FINAL TO RWY 6. WE HAD SEEN AND WERE FULLY AWARE OF THE TFC INBOUND. AFTER XING RWY 6; THE GND CTLR STARTED TO QUERY US AS TO OUR LOCATION. ONCE AGAIN; ACFT Y ANSWERED WITH OUR CALL SIGN AND THEIR LOCATION; WHICH WAS HEADING SE ON TXWY G; HEADING TOWARD TXWY L. WHEN THE CTLR QUERIED AS TO THE LOCATION OF ACFT Y; MY FO THEN WAS ALSO CONFUSED; ANSWERED; TELLING THE GND CTLR THAT WE WERE ON TXWY L HEADING FOR RWY 1 USING ACFT Y'S CALL SIGN. IT WAS AT THAT TIME THAT THE INSTRUCTING GND CTL INSTRUCTOR JUMPED IN AND TOLD US THAT WE WERE SUPPOSED TO HAVE HELD SHORT OF RWY 6; WHEN IN FACT WE WERE GIVEN INSTRUCTION TO CROSS. I THEN TOOK THE NEXT RADIO CALL AND INFORMED THE TWR THAT I WAS ACFT X AND WAS ON TXWY L HEADING FOR RWY 1; AND WAS GIVEN CLRNC TO CROSS. ONE SHOULD ALSO NOTE THAT THE ACFT ON FINAL HAD A FOREIGN PLT AND WAS TOLD TO GO AROUND DUE TO THE CLOSE PROX TO ACFT Y; AND DID NOT. THIS ONLY HELPED TO INTENSIFY THE SIT. THE ARPT WAS EXTREMELY BUSY AT THAT TIME. IT WAS ALSO DARK AND I BELIEVE THAT THERE WAS SOME TRAINING TAKING PLACE IN THE TWR. BOTH ACFT WERE CITATION EXCELS AND WERE TAXIING ALONG DIFFERENT ROUTES TO THE DEP END OF THE ARPT. THE CALL SIGNS WERE EXTREMELY CLOSE FOR ACFT X AND ACFT Y. MY RECOMMENDATIONS TO PREVENTING THIS AS TO HAPPENING AGAIN ARE AS FOLLOWS: MAKE SURE THAT ALL INVOLVED ARE FULLY AWARE OF WHO AND WHERE THEY ARE; RESOLVE ANY DOUBTS ABOUT ODD CLRNCS OR MISTAKEN ACFT IDENTS; BE PROACTIVE AS SOON AS POSSIBLE. SUPPLEMENTAL INFO FROM ACN 565607: I WAS FO AND HAD ANSWERED FOR OUR CALL SIGN A COUPLE OF TIMES CONFUSING THE GND CTLR; WHO I BELIEVE WAS IN TRAINING. GND THEN ASKED EACH ACFT TO VERIFY POS; WHICH WE EACH DID; RESOLVING THE CONFUSION. I BELIEVED. SUPPLEMENTAL INFO FROM ACN 565475: WE WERE CLRED TO RWY 1. AT ABOUT THE SAME TIME; COMPANY ACFT WAS ALSO TAXIING TO RWY 1. WE WERE THEN GIVEN AN 'IMMEDIATE' CLRNC ACROSS RWY 6. BY MISTAKE; BOTH MY ACFT AND COMPANY ACFT CROSSED RWY 6. LNDG TFC WAS ON 1 NM FINAL.