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Shortly after takeoff, the data suggest that the Left AOA vane was damaged by some foreign object, likely a bird strike. This then likely caused a short in the heating element. This would have annunciated the Master Caution/Anti-Ice lights on the forward glareshield.
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The Anti-Ice annunciation would have directed the pilots to the relevant area of the overhead panel which would have shown a "L Alpha Vane" light illuminated on the Probe Heat control panel.
So when both pilots say "Left Alpha Vane", what is going on is the very standard procedure of verbally announcing the particular annunciator that generated the Master Caution light in the first place. Not really a great mystery.
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