Quayle is now the standard Manx spelling - derived from Mac Phail, Paul's son - however I understand the name Quail is also Irish (? same derivation - those in Liverpool with this spelling are usually found to have irish origins) - there are many spellings in 17th + 18th C - see www.manxnotebook.com/manxnb/v04p130.htm

The Isle of Wight is close to Portsmouth and many Manx were in the Navy (voluntarily or otherwise - possibly a Manx name anglicised)