Hydra is said to represent the monster that Hercules slew as part of his Twelve Tasks. It had nine heads, one of them immortal, and when ever one was cut off another two grew in it's place.  There is also another story that associates it with the nearby constellations of Corvus the Crow and Crater the Cup.  Corvus was sent by Apollo to fetch a drink from a stream in the cup, but on the way back Corvus was distracted by some unripe figs.  Corvus dallied by the fig tree while the fruit ripened, but it took longer than he realised, so brought back the snake in his claws as an excuse for his delay.  Apollo was angered at this and banished the crow to the sky with the cup and snake.

Alphard, alpha (a) Hydrae, means "the Solitary one" and if one looks at it's location in the sky it's not hard to see why it got it's name - there is no other brighter star near it and it looks a bit lonely, hanging around by itself.