Narrative:

On takeoff; plane in front of us asked for a right turn to a heading of 310 for weather 3 1/2 off the departure end. During initial climb; we asked for the same heading. Tower told us to turn. Then he realized that he had us confused with the airplane that had taken off in front of us and he wanted us on a heading of 210. It was impossible to turn to that heading by then because we would fly through the cell. The controller said that he had confused our flight with the other. He then asked us to stop the climb at 4;000 ft (instead of the usual 5;000 ft for the SID). He acknowledged that it was his mistake.from what I remembered; he was calling for moderate rain about 3 1/2 from the departure end; but our radar then showed extreme precipitation (and that is the reason for asking for the turn after airborne).tower was handling 4 aircraft with similar callsigns. There was a little confusion on the ground with the tower as he was busy with the slow departure rate; spacing at different departure fixes and trying give taxi instructions for re-sequencing. Controller was busy dealing also with weather not only [on] departure end; but all around the departure corridor due to the remains of [a major storm] pushing through the area.we should have asked for more time on the ground asking for the deviation. The tower controller still handling the previous departure weather deviation; then he cleared us for takeoff and immediately cleared another plane into position on the runway at the same time. I should have asked the controller for a timeout; but us being time pressure to roll since the plane that was holding short had being given a position and hold clearance.I discussed with the first officer (first officer) later during the flight what had happened and I said to him that I should have not accepted the departure clearance since there was so much confusion on the radio and that I should have asked for a cancellation of the takeoff clearance until we could further discuss the weather at the end and what plan B was going to be. Since we were taxing opposite direction (parallel) to the takeoff runway; we had no clue that there was weather at the departure end until we received our line-up and wait and takeoff clearance.

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Original NASA ASRS Text

Title: Air Carrier flight crew reported a communication breakdown with ATC.

Narrative: On takeoff; plane in front of us asked for a right turn to a heading of 310 for weather 3 1/2 off the departure end. During initial climb; we asked for the same heading. Tower told us to turn. Then he realized that he had us confused with the airplane that had taken off in front of us and he wanted us on a heading of 210. It was impossible to turn to that heading by then because we would fly through the cell. The controller said that he had confused our flight with the other. He then asked us to stop the climb at 4;000 ft (instead of the usual 5;000 ft for the SID). He acknowledged that it was his mistake.From what I remembered; he was calling for moderate rain about 3 1/2 from the departure end; but our radar then showed extreme precipitation (and that is the reason for asking for the turn after airborne).Tower was handling 4 aircraft with similar callsigns. There was a little confusion on the ground with the tower as he was busy with the slow departure rate; spacing at different departure fixes and trying give taxi instructions for re-sequencing. Controller was busy dealing also with weather not only [on] departure end; but all around the departure corridor due to the remains of [a major storm] pushing through the area.We should have asked for more time on the ground asking for the deviation. The tower controller still handling the previous departure weather deviation; then he cleared us for takeoff and immediately cleared another plane into position on the runway at the same time. I should have asked the controller for a timeout; but us being time pressure to roll since the plane that was holding short had being given a position and hold clearance.I discussed with the FO (First Officer) later during the flight what had happened and I said to him that I should have not accepted the departure clearance since there was so much confusion on the radio and that I should have asked for a cancellation of the takeoff clearance until we could further discuss the weather at the end and what plan B was going to be. Since we were taxing opposite direction (parallel) to the takeoff runway; we had no clue that there was weather at the departure end until we received our line-up and wait and takeoff clearance.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.