We've already covered that. Aethelred was Aethelred because he had an English mother. What we call Scots is just an old, backwoods dialect of English. Completely different from Scots Gaelic.
I hope I've been clear about this, but maybe not. The idea that Aed is a translation or shortening of Aethelred has never been on the table. In Scots (not Scots Gaelic) Aethelred can certainly be elided to Aelred, but that's irrelevant.
I'm talking about having different names in different cultures. One example I gave earlier was Hrolf and Rollo. The ancestor of the dukes of Normany was named Hrolf. The French renamed him Rollo. There is absolutely no etymological connection between the two names. Another example is the Gaelic name Saorbreathach. A good, traditional Gaelic name common among the McCarthys in Ireland. In English they substitute the name Justin. No etymological or phonetic connection. We could multiple the examples endlessly but the main point is that cross-cultural names do not always have an exact correspondence.