"Ilk" is not an acronym. It is a word --- ilk--. It is common for someone to be known as "Logan of that Ilk" or whatever name they carry, "of that Ilk." It means: The same. Used following a name to indicate that the one named resides in an area bearing the same name: Logan of that ilk. [Logan of Logan]
It is also very common for many Scots descendants to carry the names of their forebears...going back to the original bearer of the name (progenitor.)
Good luck to you in your genealogical endeavors.
Lauren M. Boyd, FSA Scot
President, Scottish Information Societyhttp://www.scottishinfo.org