B737 Next Generation Undifferentiated
Communication Breakdown; Confusion
ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued New Clearance; Flight Crew Became Reoriented; Flight Crew Returned To Clearance
Chart Or Publication; Human Factors
Location at gate prior to pushback during prep. PDC not working due to full route clearance change. Both Captain and First Officer listened to clearance both of us heard the clearance to be SILOW 4 instead of SNOBL 3; and read the clearance back as such. Upon departure at check-in on [Departure]; the Controller confirmed with us that we were flying the SILOW 4; at least that is what both of us heard. I read it back as such. At 7000' we were given a turn to QUAKY which was not on the departure. This is when I questioned the Controller and figured out that they had assumed we had been cleared on the SNOBL 3. It turns out that in PHX speak SNOBL 3 and SILOW 4 sound a lot alike to two east coast Pilots. The F/O and I both heard these clearances three times from two different Controllers and still interpreted SNOBL as SILOW.Recommend name change on these two departures or phonetic spelling when the clearance is in question.  In this particular case; however; we didn't realize there was any question in the clearance.
An Air Carrier crew was cleared on the PHX SNOBL 3 Departure during a full route clearance but read back SILOW 4. A total of three clearances; include to Departure; were read back and acknowledged as SILOW 4. The crew was East Coast based not tuned to West Coast verbal sounds.