From Dach (“roof”) + Hase (“hare”). Attested in this form at least since the 17th century. The word is either an alteration of Middle Low German bönhase (“cat”, literally “loft hare”), which is found in the early 14th century (as a name and thus probably even older), or both words must go back to some ancient source. Compare similar forms in other European languages, including English, though these seem to be of younger date (?).
- “Dachhase” in Duden online