If you know your Philippine geography, then you should know that the northernmost island in this archipelago is Y’ami Island in the province of Batanes. This small island, also known by its modern name Mavudis Island, is separated from Taiwan by the 200-plus-kilometer Bashi Channel. On a clear day, one can supposedly spot Taiwan from Y’ami.
Y’ami is a remote, rocky island. To illustrate its remoteness, there’s a story that goes around saying that there was once a young man from Y’ami who wanted to marry a girl from the main island of Itbayat to the south. Y’ami is so remote that the man supposedly went to Taiwan, flew to Manila, then then to the Batanes capital of Basco, before riding the boat to Itbayat. The story is almost certainly an urban legend since Itbayat is closer to Y’ami than Taiwan is, and because the official website of Batanes says that only the islands of Itbayat, Batan, and Sabtang are inhabited.
It is interesting to note that the inhabitants of Orchid Island in Taiwan, the nearest island to Y’ami, are the Yami people, which are part of the Taiwanese aborigines. It’s highly likely that Y’ami got its name from these people, but I have no reference to back it up.