Washington state was named for our first president. This was an awkward, confusing choice. I'll get into this later.
There have been several places named for George Washington. Most obviously is the town of George, in the Columbia river Gorge in Grant county. It is the nearest post office to the Gorge Amphitheater, scene of numerous concerts and festivals. Population 501.
There's also a much larger city named for his plantation, Mount Vernon. I think there's a town of Martha, but I can't find it now.
Oregon territory's history of racism played to the advantage of what would become Washington, in that a number of early black settlers settled far enough north of the river that they could avoid most of that. Two of the most important were both named for George Washington.
George Washington Bush had been born a free black in Pennsylvania in 1779 and was named for the then hero of the revolution. He gradually moved west and worked as a voyageur and fur trapper, eventually marrying and settling in Missouri. in 1844 he and his family set out on the Oregon trail. When they eventually got to Oregon, racial violence had led to the territory enacting "Lash Laws", which allowed black people to be whipped until they went away. As a consequence, Bush and his party built a new fork to the trail, leading into what would become western Washington. This territory was still claimed by the British, but in 1846 a settlement was reached where what was then called "Columbia Territory" would be divided at the 49th parallel, which remains the border to this day. The British land north of the 49th parallel is called "British Columbia" to this day. The namesake river has its origin in the mountains of eastern BC.
Bush's large family would start a successful farm near what is today Olympia, on what is still called "Bush Prairie" in his honor. He was apparently well liked and generous toward new settlers and much of his family engaged in public service. One of his sons would serve in the state legislature. He died in 1863 and was buried in Tumwater. The Olympia airport partially covers what had been his farm, and there's a museum dedicated to him on the site.
A man named George Washington was born in 1817 in Virginia, son of a freed slave and an English woman, and raised by a white family, who moved west in several steps. Eventually they started a farm near what would become Centralia. When, 1872, the Northern Pacific Railroad made plans to pass near his property, he saw an opportunity and founded a town, which would go through several names until they settled on "Centralia". He was a proponent of fair business practices, so much that he became a trusted arbiter, and would frequently turn racist settlers into good friends through his actions.
While all of this was happening, the area that would become Washington was varyingly called Oregon or Columbia. In 1852, a group of prominent settlers would apply to congress to split from Oregon territory, with the name "Columbia". The territory would be all the land from the coast to the continental divide, in what is today Montana. Congress decided that "Columbia" would be too confusing because the capitol is called "The District of Columbia". So the applicants refiled with the name "Washington". I'm pretty sure this was meant to be sarcastic; what we today would call snark, but the congress bought it, and Washington territory would be its name, starting in 1853. In 1859, further applications split off what would become the Idaho Panhandle and western Montana, leaving the border just as they are today. In 1889, Washington became a state, with its capitol at Olympia, near Bush's farm and the south sound Geoducks.