Medium Transport; Low Wing; 2 Turbojet Eng
Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Communication Breakdown
ATC Issue All Types; Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued New Clearance; Flight Crew Took Evasive Action
Human Factors; Procedure
We were flying the BAYYY3 arrival into HOU. We were cleared to descend VIA the arrival; but to maintain FL220. We read back the altitude. We were then cleared to now maintain FL230 and we read that altitude clearance back to ATC. Shortly after leveling off we were then cleared to maintain FL200. We the PNF [Pilot not Flying] read back the new altitude clearance; PF [Pilot Flying] set the altitude in the selector and proper call outs were made. Passing FL215 the Controller asked us where are you going? The PNF replied FL200 as cleared. The Controller stated he only cleared us to FL230. (Not correct). We momentarily stopped the descent and shortly thereafter he re-cleared us to continue the descent. The Controller said it was 'not an issue and he had taken care of it.' We have tried and tried again to stress the use of full call signs; but ATC continues to use only the last 3 digits. Multiple times we have had to query ATC when multiple call signs are on the same frequency with the exact same last 3 digits in the tail number. My recommendation: quit using former company call signs and use current company call sign with the full tail number.
Medium Transport aircraft Captain reported an altitude deviation occurred while on the BAYYY3 arrival into HOU airport. It was also reported that ATC's use of incomplete call signs may have contributed to the clearance deviation.