I think "clutterbox" sounds better (perhaps because of its similarity to "chatterbox") and has better associations (perhaps it's a UK/US thing, but to me "bin"

I think "clutterbox" sounds better (perhaps because of its similarity to "chatterbox") and has better associations (perhaps it's a UK/US thing, but to me "bin" strongly suggests throwing stuff away permanently, which suggests a mere disposal service). In the UK there seem to be a company called Clutterbox (providing resources for primary-school teachers) and a product of the same name (a garden shed!), whereas Clutterbin seems not to be in commercial use anywhere.