I’m not entirely sure that something as ungainly as Ungoogleable should have been a word in the first place, but then I don’t speak Swedish (where it’s technically “ogooglebar”), so I don’t get a say either way. Still, officially speaking, Sweden has given up on a fight with Google over the word.
Ungoogleable/Ogooglebar does — or did — mean what you think it might mean, namely something that can’t be found using a search engine. Google objected to the phrase on trademark grounds, because words that become generic tend to lose their trademark status, putting pressure on the Swedish Language Council to remove it from a list of formally approved Swedish words. According to The Wall Street Journal, the council has capitulated and removed ogooglebar from a list of new words which also includes emoji and grexit. Having said that, they’re apparently not going to formalise its removal either, noting that Google doesn’t own the Swedish language, so native Swedish speakers may just continue to find things ogooglebar.. ish. I suppose. Like I said, I don’t speak Swedish.
Googling something — as a form of saying searching for something — is certainly something that appears to be taking hold in the English language too. Is it part of your lexicon, and are Google within their sensible as well as legal rights on this issue?