I had version 1.3.5 and upgraded to the latest version according to instructions. All went smooth but when I check the MySQL tables I still see a 1.3.5 prefix in front of the coppermine tables? Is this normal?
That's fine. Upgrades don't change the table prefix.
Ok but will a fresh file install recognize it?
recognize what? Don't perform a fresh install unless you need another separate gallery on your site. The prefix is just what the name suggests: a string that is being used to tag the tables created in the database. It could be "foobar" or whatever you like. If you perform a fresh install, you're being prompted what table prefix you want to use, that's about it. Don't perform a fresh install if everything works as expected, no end user will ever see what prefix you have chosen.