The word crap is actually of Middle English origin, and first appeared in the Oxford English Dictionary in 1846 under a reference to a crapping ken, or a privy, where ken means a house.

Its most likely etymological origin is a combination of two older words, the Dutch krappen, to pluck off, cut off, or separate; and the Old French crappe, or siftings or waste or rejected matter, from medieval Latin crappa, chaff.

As Thomas Crapper launched his company in 1861 and only gained fame much later, there is therefore no direct link between his name and the colloquialism, except one of coincidence.