The son and heir of KingSiriondil of Gondor, who was famed for his naval exploits, and founded the line of the Ship-kings that continued until the time of Hyarmendacil I. His Queen was the notorious Berúthiel, who Tarannon was forced to send into exile, so that he died without an heir. He was succeeded instead by his nephew, who ruled as the second of the Ship-kings, Eärnil I.
The date of Tarannon's birth appears only in The History of Middle-earth volume 12, The Peoples of Middle-earth. It cannot therefore be considered completely reliable.
'Royal gate' seems a strange choice of name, and doesn't appear to connect with Tarannon's life in any obvious way. It's possible that the name has some deeper etymology, but it seems to combine the simple Elvish elements tar 'royal' and annon 'gate'.