Upvote:1
It's fine, at least as far as the airline is concerned. This situation is very common and airlines are quite used to dealing with it, plus all they care about is whether you will be let into your destination.
So:
Now the one catch is that Bahrain apparently does not recognize dual citizenship, so if the "Canadian" name on your boarding pass differs significantly from your "Bahraini" name, or they notice that your Bahraini passport doesn't have an EU visa, Immigration may start asking awkward questions. The traditional dodge for this is to fly via a third country with two separate tickets, eg. Bahrain->UAE (with your Bahraini name) and then UAE->EU (with your Canadian name).