Of the twenty or so species of Lycopus, Lycopus europaeus is perhaps the most broadly distributed, occurring across Europe and Asia and into northern Africa. It has also been introduced into North America and New Zealand.
Species of Lycopus often have the name water horehound in their common names (e.g., European water horehound in this instance; other common names include gipsywort and bugleweed). The “water” part of the name is derived from the typical habitat: the sides of rivers and streams, and in ditches, marshes, and fens. That said, these plants have no problem growing in our Physic Garden, where they experience a summer-drought climate.
With respect to “horehound”, the name is first of all in reference to a different species in the mint family to which the group bears a strong resemblance, Marrubium vulgare. The Wikipedia entry for that species explains the common name, which has nothing to do with dogs:
The Oxford English Dictionary derives the word from two Old English forms: “hoar” (“white,” “light-colored,” as in “hoarfrost”) and “hune” a word of unknown origin designating a class of herbs or plants. The second element was altered by folk etymology.
The name gipsywort may have also piqued your interest; the species is thought to be used / have been used by the Romani people as a dye for their skin and/or fabric (the juice dyes black), though I am finding it difficult to source a firsthand or reputable secondhand account.