The original meaning of the letter name is unknown, but it is likely an artificially altered pairing with Idad, much like Gothic pairþra, qairþra.
Medieval "arboreal" glossators assign crand fir no crithach "'true tree' or aspen" (Crann Creathach in modern Irish) to this letter, though this has little to recommend it by way of either the kennings or the etymology.
Given éo as the likely Old Irish word for "yew tree" (see idad) and the variant forms of Old Irish é/éo "salmon", we can understand the "exchange of friends" kenning; at the time the kenning was constructed this would have been understood as a word play involving exchange of meaning between the paired edad (é/éo salmon because of the value of the letter [e]) and idad (éo yew).
McManus also suggests that "brother of birch" may be a kenning erroneously displaced to the penultimate of the original twenty letters, from the penultimate forfeda which had an original letter name pín [p] that when changed later to ifín necessitated the invention of peithe [p] also called beithe bog "soft beithe", hence "brother of birch".
In the medieval kennings, called Bríatharogaim or Word Ogham the verses associated with edad are: érgnaid fid - "discerning tree/chap" in the Bríatharogam Morann mic Moín commaín carat - "exchange of friends" in the Bríatharogam Mac ind Óc bráthair bethi (?)