Owning a Logo, and the Rights to use it? Legal Rights etc.?

Okay me and my father are starting up our own Filming Buisness Pedro'S Productions, Filmings parties, weddings, graduations, etc. and well were are comming up with a logo but i would like to know about like the lega rights. We want to make sure no one can use our Name or Our Logo. Please answer quick. Help us out :)