For example, someone born in London but who moved to Wales at a young age and therefore wants to be known as a Welshman rather than an Englishman?
"Native" comes from the Latin word for 'born'. A person born in London can never become a "native" Welsh person, except maybe, at a stretch, to Welsh parents who were visiting. As S Conroy notes, a person who moved to Wales at a young age might come to "identify" as Welsh. Your question ignores 50% of the human race by supposing that the imaginary person always wants to be a "Welshman".