According to Henry Harrison in ‘Surnames of the United Kingdom: A Concise Etymological Dictionary’ (Baltimore: Geneological Publishing Company, 2013) the last name Elderkin could have been a nickname for someone who was a dweller at, or near, an elder tree.
According to Eldson Coles Smith in the New Dictionary of American Family Names (New York, Harper & Row, 1956) the last name Elderkin comes from the noble Boernician clans of the Scottish-English border region. It is a name given to a person who was the elder of two people bearing the same name. The dictionary also suggests that the name could be derived from the Old English word ealdra, which means elder.
It could therefore be speculated that the origins of the name should be traced back to include the last name Elder, and even references to the suffix ‘ye elder’. I am not intending to divert that far, not to investigate other last names derived from Elder such as Eldarson, Elderson, Ellderson and Eldersham.
Thankfully the predominant spelling is Elderkin, and very few alternative spellings are used, making searches much easier. Here are some of the variations I have found (which may of course be down to mistranscription, clerical embellishment, error, or preference).
16th century records: Elderkyn, Elderkey, Elderkine, Elderker, Elderkins, Elderkines.
17th century records: Elderskin, Elderkyn, Ellderkyn.
18th century records Elderkinn, Elderk, Elderken.
19th century records: Elderskin, Elderkan, Elderken, Elderkens, Elderkim, Elderkins.
Some early instances I have found using the name Elderkin and its alternative spellings include:
1564 Jone Elderkey baptism, London
1572 Ralf Elderker burial, Cheddington, Buckinghamshire
1574 Thomas Elderkyn probate index, Northamptonshire and Rutland
1592 Thomas Elderkine baptism, Dean, Bedfordshire
1595 Briget Elderkin baptism, Dean, Bedfordshire
1595 Johannes Elderkyn baptism, Sutton St James, Lincolnshire
1600 Thomas Elderkin baptism, Sutton St James, Lincolnshire
1612 Anne Elderkyn baptism, Harrow on the Hill, London
1614 John Ellderkyn baptism, Wrangle, Lincolnshire
1638 Elizabeth Elderskin baptism, Sutton St James, Lincolnshire