While ystematically adding the websites of all the subdistrict administrative organizations (TAO) in Nakhon Si Thammarat province to my XML, at first I could not find the one for Tha Phaya, Pak Phanang district. The only website which contained the term "องค์การบริหารส่วนตำบลท่าพยา" was the article on the district in the Thai wikipedia. This seemed strange, as even for TAO without a website there usually are some pages using the term. After a bit of searching I finally found the website at thapaya.go.th - the reason I could not find it before is that it is spelled "องค์การบริหารส่วนตำบลท่าพญา". The two letters Yo Yak (ย) and Yo Ying (ญ) are absolute equivalent, so this spelling change does not change the pronunciation at all.
However all of the sources from the Department of Provincial Administration (DOPA), e.g. the geocode list or the population statistics all use the spelling ท่าพยา. Also, the original announcement in the Royal Gazette on the creation of the TAO (see Item 699 on page 71) uses ท่าพยา, and I haven't seen any announcement on a spelling change. On the other hand, ThaiTambon.com uses the same spelling as the TAO, indicating that not only the TAO but also the Tambon changed its spelling.
Though I had not much hope of a reply, I tried to ask the TAO for an explantion, but thins time the email wasn't ignored - because they misconfigured the mail server so any email sent to firstname.lastname@example.org bounced right away. And I doubt anyone would ever find my question in the forum, as it seems only frequented by spam bots.