North German and Dutch: topographic name from Middle Low German hage(n), Middle Dutch haghe ‘enclosure’, ‘hedge’.
German, Dutch, and Danish: from a Germanic personal name, a short form of the various compound names formed with hag ‘enclosure’, ‘protected place’ as the first element.
German: nickname from Middle High German hagen ‘breeding bull’.
Jewish (Ashkenazic): of uncertain origin; perhaps the same as 1.
English: from an Old Scandinavian or continental Germanic personal name Hogni ‘protector’, ‘patron’ (Old Norse), Haghni (Old Danish), Hagano (Old Germanic).
Norwegian: habitational name from any of numerous farmsteads so named, from the definite singular form of hage, from Old Norse hagi ‘enclosure’.
Swedish: ornamental or topographic name from the definite singular form of hage ‘enclosed pasture’.
Almost universally, they claim to “like themselves” in spite of obvious indications of low self-esteem.