I love these kind of questions!

Yes, multiple proposals have been made to name Western states after presidents or other founding figures.

Lincoln was a proposed state that would have consisted of the Eastern 3/4s of Washington and the Panhandle of Idaho. Idaho proposed it in 1901, and although it failed, another proposal was made in the 20s that consisted of the original proposal with the addition of Western Montana.

North Dakota was originally proposed to be called Lincoln, suggested by Republicans, but Democrats weren't fond of it.

When they were considering the name of what is now Wyoming, one suggestion was the "Lincoln Territory"

A state of Lincoln that consisted of most of South and Western Texas was proposed during reconstruction, but never passed.

Jefferson was a proposed state that would consist of the other half of Texas, splitting Texas into Lincoln and Jefferson.

Jefferson was also a proposed state in 1941, and consisted of South Oregon and Northern California, areas whose populations are very different from their state's population centers, and who have historically been unrepresented in state government, with their state's dominated by LA and Portland respectively. This idea was revived in 2016 by Northern Californian counties who were heavily Republican, feeling their vote doesn't matter in the heavily democratic California.

There was also a Jefferson Territory that technically existed from 1859-1861, and has its own government, though it was not seen as legitimate by the US. It consisted of land from multiple different territories, and was dissolved when the Colorado territory was created.

Moving East, a State of Franklin was another unrecognized territory, and consisted of the Eastern portion of Tennessee. Found in 1784, its government was dysfunctional and it was incorporated into the Southwest territory by 1790.

I can't think of any other examples on a state level, but here you go.