The many spellings of the name (Adkyn, Adkyns, Adkynson, Atkyn, Atkynson, Adkinson, Attekson, Addykin, Akin, Akins, as well as the above four) came about during the Sixteenth, Seventeenth, and Eighteenth centuries. Many people, because of their extremely primitive living conditions, did not learn to read and write thus when some government official (census taker, court clerk, etc) needed to record the name they did it phonetically or simply as they thought it should be.
A variation is given in
http://www.searchforancestors.com/surnames/origin/a/atkins.php
Camden derives it from At, a familiar abbreviation of Arthur, and kins, a diminutive, signifying a child, having the same meaning as the German kind, a child, an infant, i. e., the son of Arthur, so Wilkins, Simpkins, etc
