While you are correct that the Philippines at its current extent did not exist as a single coherent entity before Spanish colonization, I think its important to note two things. Firstly, that there were smaller political entities that existed before the Spanish like the Sultanate of Sulu and the polity of Maynila, and secondly, that while the Spanish might have claimed the entirety of what is now known as the Philippines, they certainly did not control every island, and there are parts of Mindanao, the southernmost island, that were never fully brought into the fold. Raiders from Mindanao were a regular concern of the Spanish that they were never able to pacify due to many factors such as the terrain and the allies that they might muster from their fellow Muslim rulers, which indicates that they had an independent society.

All this to say that there wasn't a name used for the entire Philippine islands before the Philippines that people now would agree to. An interesting comparison would be the Holy Roman Empire, which might also be characterised as disparate politico-geographic groups of relatively small size that had a history of relations between each other, but one thing they had that the Philippines did not was a common language, or at least a family of mostly mutually intelligible languages, so that the name Deutschland or Germany isn't terribly offensive to anyone. If you called the Philippines the Lupang-Tagalog or even Lupang-Tao the other ethnic groups would protest.

I also think that it would be interesting to note why the name Philippines was kept after the Spanish left. There was a revolution against Spanish rule, but this was not the reason they left. They left after the 1898 Battle of Manila, a mock battle allowing the Spanish to leave with some grace and leaving the door open for the Americans, as outlined in the Treaty of Paris. Which means that the revolutionaries, who initially fought alongside the Americans which they had thought were their allies, had some ideas on better names for their country that were disregarded as the new colonial overlords consolidated their rule. After the Americans left, there were some attempts by Filipino politicians to change the name to Maharlika, but they were shot down due to it being a Tagalog word, which is just one of the many, many languages in the Philippines.

While I imagine he wasn't the one to decide the name, William Howard Taft was the first American Governor-General of the Philippines, a few years before he became Secretary of War then President.