GA PLT ENTERED RWY WITHOUT ATC APPROVAL. POTENTIAL CALL SIGN CONFUSION.

Narrative

WE WERE AT 3500 FT MSL; ABOUT 8 1/ MI N; INBOUND TO LIVERMORE ARPT (LVK). THERE WAS CONSIDERABLE TFC ACTIVITY AT LVK. THE TWR CTLR INSTRUCTED US TO MAKE A R BASE ENTRY TO RWY 25R. AS WE TURNED ONTO FINAL APCH; THE TWR CLRED US FOR LNDG. WE RESPONDED WITH CLRED FOR LNDG; FULL STOP TAXI BACK. THE TWR CTLR DID NOT RESPOND; BUT CONTINUED TALKING TO OTHER ACFT. WE LANDED ON RWY 25R AND TOOK THE FIRST OFF RAMP AND TURNED R ONTO THE TXWY AND PROCEEDED WITH OUR TAXI BACK TO 25R. AT HALF WAY ALONG THE TXWY; THE TWR CTLR ASKED IF WE WERE ON TWR FREQ OR GND FREQ 121.6. WE RESPONDED THE WE WERE STILL ON TWR FREQ 118.1. THE TWR CTLR THEN PROCEEDED TO INFORM US WE DID NOT HAVE A CLRNC TO MAKE A TAXI BACK AND THAT WE SHOULD BE IN CONTACT WITH GND CTL; BUT DID NOT INSTRUCT US TO CONTACT GND CTRL. THE VERBAL TONE OF THE TWR CTLR'S VOICE INDICATED THAT HE WAS VERY UPSET WITH US. BY THE END OF THIS VERBAL EXCHANGE; WE WERE AT THE RUN UP AREA FOR RWY 25R. WE REMAINED ON TWR FREQ. WE TAXIED UP TO THE RWY 25R HOLD LINE. AT THE SAME TIME; ACROSS THE RWY; A KING AIR TAXIED UP TO THE OPPOSITE SIDE RWY 25R HOLD LINE. I CALLED THE TWR RPTING THAT WE WERE READY FOR TKOF. SO DID THE KING AIR. THE TWR CTLR WAS USING ONLY THE LAST THREE CALL SIGN LETTERS IN COM WITH THE ACFT IN OP AT LVK. THE LAST THREE LETTERS IN OUR CALL SIGN AND THE CALL SIGN OF THE KING AIR VARIED ONLY BY THE DIFFERENCE OF THE MIDDLE DIGIT. WE THEN HEARD A CALL OVER THE TWR FREQ WHAT WE BELIEVE TO BE OUR CALL SIGN TO TAXI INTO POS AND HOLD.' WE RESPONDED WITH 'CALL SIGN; POS AND HOLD