Brand names seeping into the lexicon

Is there a word for when a trademarked name works its way into a language as the general word used for that item? A few examples in English I can think of are Bandaid, Kleenex, and Thermos. In German there's Tempotuch (a brand of pocket-sized tissue packs) and a few others. Is it just a subset of metonymy, or is this something entirely different? I'm also curious about examples from other languages.