Plus a lot of this NP PCT stuff goes on at length about permits etc, but misses the simple stuff, and assumes you understand all the ins and outs about permits etc
Sara, the PCT association gives a permit that I believe all the rangers recognize along the entire PCT. So if you started up in Washington, it would technically be valid all the way to your southern end, through Yosemite to Mt. Whitney. (...Reading Fishmonger's link above, I see it is only available to hikers planning to hike 500+ miles.

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If you plan on using the Main Mt Whitney Trail to go in or out via Whitney Portal (near Lone Pine, California), there is an extra $15 charge required.
Lots of PCT hikers jump around, leapfrogging sections when the snow is too deep, for example, in June in the JMT section. They never worry about the permits.
The alternative, to go without the PCT permit, is to snag a walk-in permit. They are available, to start in Yosemite as well as starting from Whitney Portal. If those options are what you want, let us know, and we can give you more info.