Occasionally people would be known by two surnames - usually due to illegitimacy, but not always. I have a whole family of 'BOWDEN alias WILLIAMS'.
A Vincent BOWDEN married an Ann WILLIAMS in 1786. However, before their marriage they baptised 2 children:
"William, a base child of Ann WILLIAMS, born at Vincent BOWDEN's house in Brodsworthy, was baptized January tenth 1781. She says she was born at Breock in Cornwall and came from thence into this county."
Parish Registers, Meavy, 20 Sep 1782.
"John WILLIAMS another base child of Ann WILLIAMS baptised." (died in infancy)
The first child - William - was baptised William WILLIAMS and yet became known as William BOWDEN alias WILLIAMS on later Church register entries. One of his children was even baptised:
"28 Jan 1827, Meavy: BOWDEN John Bowden, son of William Williams & Mary, Labourer."
and his daughter's marriage entry reads:
26 Dec 1859.
"John William Lillycrap (of Almondsbury, Gloucester) to Mary Bowden alias Williams, father William Bowden alias Williams."
Try working that one out!
So, my advice would be to keep an open mind on the surname. If you don't strike lucky with the CORK name - try LOVEDAY.
By the way, I should have suggested COR*K* - I note some spellings are CORKE.