Date: 202003
Local time of day: 1201-1800
Location: ZZZ.ARTCC, US
Light: Daylight
Aircraft: Commercial Fixed Wing
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Descent
Airspace: Class A ZZZ
ATC / advisory: Center ZZZ
Second aircraft: Commercial Fixed Wing
Reporter organization: Air Carrier
Reporter function: Captain; Pilot Not Flying
Reporter qualification: Flight Crew Air Transport Pilot (ATP)
Human factors: Communication Breakdown
Second reporter function: Pilot Flying; First Officer
Anomaly: ATC Issue All Types; Conflict Airborne Conflict; Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Clearance
Detector: Automation Aircraft TA; Person Air Traffic Control
When detected: In-flight
Result: Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance; Flight Crew Took Evasive Action
Contributing factors: Environment - Non Weather Related; Human Factors; Procedure
Primary problem: Procedure

Narrative: Center gave us a clearance to descend from FL390 to FL290. I read it back and we started a descent. As we were descending we did get a TCAS alert of traffic less than 1;000 feet; but the PF (Pilot Flying) went to Vertical Speed to slow our rate down to avoid an RA. About 400 feet in descent; ATC queried us if we were still level at FL390. We said no that we were in a descent to FL290. He proceeded to say that we were not supposed to descend. I told him that's what he gave to us. He said no it was for our Company [callsign].  He asked them; and of course; they were descending to FL290. So we must have gotten blocked on our transmission. That's probably why ATC didn't correct us because he only heard [the callsign]. The frequency was very congested due to Center and surrounding airports being closed at the time; and that was also why we were running late. There was no issue with the traffic off of our right wing that we got a Traffic Alert on. Our Company asked if their altitude was corrected because of doubt. ATC said 'yes.'  Later ATC said that it was not a problem.


Second narrative: We were cruising at FL390; I had left to go to the lav. Captain was flying while I was out of the cockpit. When I returned and put on my headset; I heard him say descend and maintain FL290. It seemed early to descend; but the previous leg they had made us descend early and well; these are crazy days. I accepted aircraft control and hit Altitude Intervention and started the descent at around 1;000 FPM. After descending about 400 feet; we both saw a yellow icon on the TCAS display that was 700 - 600 feet beneath us; at that point. I immediately went to Vertical Speed and slowed our rate of descent as the traffic passed.We never got a TCAS RA or red display; [and] at that time Center called and said '(Callsign) are you descending?' The Captain replied 'yes' that we had received such a clearance; the Controller disagreed - said it was meant for another aircraft. In any case; the Captain read it back as if it was our clearance and was not corrected. They then told us to descend to FL370; and we did that and continued on our way.


Synopsis: Air carrier flight crew and an enroute Controller reported an airborne conflict occurred when the flight crew took a descent clearance intended for another aircraft. Controller suggested that increased workload associated with COVID-19 procedures contributed to the event.