MRH90 Name vs Callsign
COBRA is the callsign used by the RAN Aircraft Maintenance and Flight Trials Unit (AMAFTU). It can equally apply to a Seahawks as an MRH90. The callsign for 808 Squadron is "Poseidon" a reference to the Squadron crest - "Trident" was not available as it is a little used RAAF MPA formation callsign.
The name TAIPAN was not universally popular (who names an aircraft after a snake?) but was decided by a committee of senior Army personnel.