Native (US-)American Legend. Who knows the heroes' names?

Question

I am looking for the names of the 3 main characters in this Native American Legend. To my knowledge the legend is from the Northeast of the US.

There was a woman who loved a young man and wanted to marry him. However, another man, too, wanted her to become his wife. It was decided that both men should swim across a very wide river and bring her berries from a tree that hung its twigs over the water at the other side.
Her lover turned out to be the better swimmer, however, on the way back he was stabbed by his opponent who wrestled the berries from his hand and left him to drown.
When he returned to the shore with his trophy, totally exhausted, the woman killed him by kicking him back into the water and then drowned herself to be united with the man she loved.

What were the names of the three persons? If I recall correctly, a river, or a town or state was named after the woman.

(I am looking for the Native American names, not any English translations)

The legend of Lake Ronkonkoma is similar, but Ronkonkoma an her lover were drowned by malevolent spirits. (see this website: http://sayville.8k.com/folklore.htm ).
In the story I am loking for no supernatural being is involved, it's a purely human tragedy - the normal story of jealousy and having to stick to your socity's rules as much as you may dislike it.

Answer 1

Running Bear loved Little White Dove and their love would never wain.....

Answer 2

Big chief Swims Good
Heap bad Stab in the Back
and
Princess Erie

Answer 3

Pocahantas is Native American...Chicago got its name from the Indians...so did Texas=Tejas....sorry dont know the answer to this one..but would love to read later what it is...Love your question...very interesting