Loosely, I suppose. The U.S. Department of the Interior has, for a very long time, had specific definitions of what falls into the categories of Insular Area Political Organizations: https://www.doi.gov/oia/islands/politicatypes. But unlike the Philippines and Puerto Rico, I don't believe there was any political action dealing with Guam following the ceding from Spain and up until 1950 that made the island anything other than an "unorganized territory." They were basically a military waystation that had been transferred to the control of the U.S. Navy.
So my conundrum is WikiTree's guidelines: "Our guiding principle is...'use their conventions instead of ours.' Applied to locations, this means using place names in native languages and using the names that people at the time used, even if they now no longer exist."
I'm still stuck on Karen's question because the Data Doctors regularly debate location minutia for the sake of accuracy in following that guiding principle. The indigenous Chamorro name for the island is "Guåhån." Magellan called it Islas de las Velas Latinas in 1521. I can't find anything specifically addressing it, but I believe the island came to be called "Guam" after the indigenous "Guåhån" pronunciation sometime around 1668 when Spain began colonization of it as part of the Spanish East Indies. Guam wasn't officially made a U.S. territory until 1950, and I rather think--but have no evidence--that no one in Guam from 1899 to 1950 called their island "the Territory of Guam" or the "United States Territory of Guam." Today, if you send a letter to any U.S. territory, from American Samoa to the Marshall Islands, you use a two-character "state" abbreviation, a five- or 10-character zip code, and the country is "United States" (Guam is abbreviated "GU"; the zip code of the capital city, Hagåtña, is 96910...don't ask me why I looked that up <grin>). And that WikiPedia article referenced earlier, other than the disambiguation comment at the top, never refers to it as "the Territory of Guam," only Guam.
So I'm still kinda stumped. If I had to guess what Guamanians called their home in 1908, it would be Guam. :-)
(I have actually set foot on Guam a couple of times, but otherwise have no dog in this hunt. I'm just interested to see what the final verdict is.)