my name and my father's

It is correct.

As Philip said, it's correct, but I cannot imagine any normal situation in which a police officer would ask for my father's name. If any police officer asked me for that information,, I would refuse to respond

And that's why I have put something in my signature long ago.

Thank you, Sir.

Adding to what fivejedjon said:
Generally a policeman in American asks for your driver's license and vehicle insurance form, then they 'run the numbers' on their computer. When they come back, they will either say, "Get that tail light fixed," or they'll have a ticket book in their hand "I'm going to have to give you a citation," or they'll have their hand on their gun, and yell, 'Get out of

In Canada, the police have no legal right to simply stop you and ask for ID, unless they have reasonable grounds to justify their action. In other words, it's not a police state like you see in the movies, where the police go around the streets routinely demanding 'Show me your papers!"