Same entry already in Hesychius (iota215), where Latte regards it as generated by instances of the headword in Homer (e.g. Iliad 1.124).
The older forms of the verb oi)=da have the zero-grade of the root in the plural. In the first person plural, i)/dmen was replaced with i)/smen (iota 646) by analogy with i)/ste, and by oi)/damen (the word used to define the term here) by analogy with oi)=da in Ionic and later koine. Smyth, Sections 794-799 (web address 1).
See also iota 611, iota 612, iota 615, iota 637, iota 646, iota 680, iota 702.