No, Canary Wharf is not so named because it was the centre of London’s lucrative trade in canaries.
Rather it received its name from the fact that it was at a quay here that ships from the Spanish Canary Islands and the Mediterranean landed laden with cargos of fruit.
The wharf, part of the West India Docks on the Isle of Dogs, was built in 1936 by Fruit Lines Limited and a warehouse the following year.
The area where the wharf was once located was redeveloped under a massive regeneration project starting in the late 1980s and is now one of London’s key financial districts, filled with modern, multi-storey office towers and home to the second-tallest tower in the UK, One Canada Square (seen above with the pyramid-shaped roof).
Exploring London 
Thank you! When I lived in the UK, prior to the renewal of Canary Wharf, nice girls would not have walked around that area at night. So I find it fascinating that the wharf, part of the West India Docks, only started operating as late as 1936 and 1937. It seemed much older.
Clearly no-one would have been investing in wharf infrastructure in 1936 unless they thought there were still good profits to be made.