If you are not sure if local db is installed, or not sure which database name you should use to connect to it - try running 'sqllocaldb info' command - it will show you existing localdb databases.
Now, as far as I know, local db should be installed together with Visual Studio 2015. But probably it is not required feature, and if something goes wrong or it cannot be installed for some reason - Visual Studio installation continues still (note that is just my guess). So to be on the safe side don't rely on it will always be installed together with VS.