[Facts] Re: Aden and Adin
I am sure our resident biblical scholars will have more to say, but Adin is found in the Bible as a man's name (e.g. in Ezra 2:15). So its use among your ancestors was very likely as nothing other than an obscure biblical name which caught someone's eye, and Aden may have been just a spelling variant.
Aden is also the name of a gulf in the Arabian Sea, near the Suez Canal. It's interesting that it started showing up in the SSA in the 1880s. The building of the canal in the 1860s may have called parents' attention to it as a possible baby name.