The body of Christopher Batty, 64, from Whitby was found near to the East Pier.
His death is not being treated as suspicious, however officers are conducting enquiries to determine his last know movements.
They are appealing for anyone who knew Mr Batty or saw him between Tuesday January 7 and Saturday January 11 to contact them, as they may hold information which would assist officers.
On the day he was found, Mr Batty was wearing dark blue trousers and a khaki coloured light weight jacket, which he may of been wearing with the hood up.
Anyone who can assist is asked to contact North Yorkshire Police on 101 select option 1 and pass the information over to the Force Control Room – please quote reference 12200005826.
Information can be passed to Crimestoppers anonymously on 0800 555 111.