When I look at the city of Montral on the Openstreetmap original map, all street names are there.
But when I download the Quebec province data from http://download.geofabrik.de/osm/
only few street names are available in field “name”…
The Geofabrik extracts are updated daily, and should contain all of the OSM data in that area.
Can you give a link to a specific street name that is missing?
Note that due to the licence change, there has recently been some data removed. I don’t know how much it affected Quebec, but it may have removed some names.