This is certainly a rare surname. Any surname commencing "Exten-" is very rare, with only three listed in the British Isles, and scarcely any others world wide. The only one which comes anywhere near on spelling and pronunciation is the almost equally rare surname of Exten. This is a dialectal variant of Exton, a locational surname from any or all of the four Exton villages in England. These are in the counties of Rutland, Devonshire, Somerset, and Hampshire. All have the same meaning of "A place (tun) on water (esce)" from the pre 7th century Olde English "Esce - tun". We think it doubtful that Extence derives from Exten, but it is possible, indeed anything is possible with surnames. Extence is only recorded once in the surviving church registers of the city of London for the 19th century. This would suggest that it was an immigrant name, and indeed this is very possible, except for two problems. The first is that the recording is very "English". It appears in the register of St Pancras Old Church, in the city of London, on April 7th 1872 when one George Extence married Martha Eliza Jackson, and secondly we cannot trace a surname similar to Extence in any of the world dictionaries of surnames.