There are several entities that are or were called "Wawona".  These
include but are surely not limited to:
1) the Wawona Lodge (now Pilgrim Pines Mayflower Lodge) in Swanzey;
2) the Wawona Lodge in St. Germaine (formerly part of Woodruff,
Wisconsin), which was torn down
3) Wawona, California, in Yosemite
4)the Wawona Lodge (now the Bavarian Lodge) in Big Bear, California; and
5) the Wawona, a fishing / lumber schooner presently in a ship museum
in Washington state.

The word "Wawona" means "Big Tree" according to
http://en.wikipedia.org/wiki/Wawona,_California

My question is:  Are the various lodges and ship mentioned above named
after the town, or how did they come to be known as "Wawona"?  As much
detail as possible is desired.