Date: 202010
Local time of day: 1201-1800
Location: ZZZ.Airport, US
Flight conditions: VMC
Aircraft: Small Aircraft; Low Wing; 1 Eng; Retractable Gear
Operator: Fractional
Operating under: Part 91
Flight plan: IFR
Mission: Passenger
Flight phase: Taxi
ATC / advisory: Tower ZZZ
Reporter organization: Fractional
Reporter function: Captain; Pilot Flying
Reporter qualification: Flight Crew Commercial
Human factors: Workload; Distraction; Communication Breakdown; Confusion; Situational Awareness
Second reporter function: Pilot Not Flying; First Officer
Anomaly: ATC Issue All Types; Deviation / Discrepancy - Procedural Clearance; Ground Incursion Runway; Ground Incursion Taxiway
Detector: Person Flight Crew
When detected: Other Post Flight
Result: General None Reported / Taken
Contributing factors: Environment - Non Weather Related; Human Factors; Staffing
Primary problem: Staffing

Narrative: While operating Aircraft X into ZZZ on a program flight using the Company X ABC callsign we landed on Runway XXL and received the normal 'Left at Taxiway 1; cross Runway YR; hold short Runway YL' instructions from Tower after landing around XA:30Z. Upon approaching Runway YR we heard over the radio '[muffled] XXX#CA [callsign] cross-Runway YL on Taxiway 1 and Taxiway 2 to park.' The PIC; who was Pilot Not Flying (PNF); hesitated with a read back because the call sign was slightly muffled due to radio static; but the instructions and cadence made sense that they were for us; since we were the only aircraft on Taxiway 1 in that position to follow the instructions. So he read them back and I the SIC and IP (acting as Pilot Flying doing training in new aircraft) continued to cross YL and continued Taxiway 2 to park.Upon parking and getting out of the aircraft [and] the more I thought about it the more something seemed off. [I found out] Tower did use the wrong callsign; they used the Company Y CA [callsign]; as Company Y CA cross YL and Taxiway 1 to park.'Contributing to this situation was the crew fatigue and us not being 100% on our game. Also; the Controller had a high workload as he appeared to be working both Tower and Ground Control positions.Although the instructions were most likely for us as our callsign was somewhat similar this scenario brought up a lot of other important facts to point out. We as a crew should never assume a runway crossing instruction is for us unless our call sign is 100% specifically used without a question. If we had any doubts about the instruction; we should have stopped and ask for clarification prior to proceeding.As for the Tower Controller; he was working both Ground and Tower; which makes for a high workload; as ZZZ was experiencing a traffic push at that time and he was getting busy. His misspeaking could have caused an incident or incursion. Lucky for us Company Y CA landed 30 minutes prior to this incident taking place. It is possible the Controller had an old strip lying around or just had that specific call sign on his mind. In any case; ATC should consider increasing staffing levels and not having a single Controller work both Tower and Ground positions; except during very low traffic levels. Air traffic loads have increased significantly from the COVID lows experienced several months ago.


Second narrative: [Report narrative contained no additional information.]


Synopsis: Flight crew reported crossing a runway; taxiing to parking; while not sure if the clearance instructions were for them due to Tower muffling the callsign.