Is the Poseidon Underwater Resort named after Poseidon? If so, why did they choose to name it after Poseidon and what it means.I am doing a project...

I'm assuming you're talking about the place in Fiji that comes up on Google...

It doesn't say that it is named after Poseidon, but it surely must be.  The way you can tell that is that A) it's an ocean thing and he's god of the ocean (which is why they'd name it that -- the name makes people think of the ocean) and B) their logo is a trident which is one of his symbols.

As for other stuff named after Greek gods, the United States' program for going to the moon was named after Apollo.  And the Nike company is named after the goddess of victory.  The word "erotic" comes from the name Eros.