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I've been making up little headcanon stories about my protagonist for a while now, but with the advent of character customization options being more robust, I've developed a singular character that canonically encompasses Alola and Galar.
Gwen is from Kanto but ethnically she's Johtoan. Came to Alola to visit her aunt (The mother in Alola is not actually her mother) but then gets embroiled in the Aether scandal as well as the dimensional rifts. She probably would have left it to someone else, but she had fallen for Lillie and so most of what she did to overthrow Lusamine and investigate the portals and Ultra Beasts was for her sake. She was uncomfortable resting on her laurels as the first Alolan League Champion, so she ceded her position to manage the Battle Tree instead, working with Hapu and others to build a small community of passionate battlers and workers to maintain the facility on Poni Island.
When Lillie decides to travel to Kanto to begin her journey, Gwen offered to accompany her, but Lillie refused the help because she wanted to do it herself without any assistance (for once). Disappointed, Gwen became a bit depressed until she decided to begin a new journey of her own in Galar. A region with a supposedly unbeatable champion proved to be an excellent training ground, and due to Galar's televised matches, Gwen has become pretty famous. She's outspoken about her desire to relocate the Galaran Battle Tower away from a Gigantamax hotspot, but the cost and logistics of such an undertaking as well as backlash from Macro Cosmos prohibit it. Gwen will likely not stay in Galar much longer, as she isn't enjoying the disparity between how much of a celebrity she is and what change she can make in the world. Maybe she'll head back to Kanto and see how Lillie's doing...
Oh and her hair is snow-white because she's a faller, the dimensional rifts in Alola bleaching all the color out of her hair for some reason.