It’s called “hundflapper” in Swedish. Kind of, at least people might understand what you mean. My sister mentioned she very much likes that sound. So found a short recording of it and cleaned it up and normalized it, in case she or someone else might want it. There are fewer examples online than you might think, most of the dogs shaking themselves dry are set to music or in slow motion without sound.

Hundflapper (Ogg Vorbis, 130 Kb)
Hundflapper (flac, 411 Kb)
Hundflapper (mp3 320kbps CBR, 175 Kb)