Everyone has ALL 12 Signs in their personal unique birthchart. And real astrology is about the birthchart with all 40-50 factors in it.
What you are are talking about when you talk about someone's "zodiac sign" is ONLY their Sun Sign. Merely one factor. The ONLY factor that can be found with just the month and day of birth .. instead of the precise moment and place of birth and extensive calculations.
And, often, in any particular birthchart, the Sun (and its Sign) is NOT the dominant influence on their personality.
“Many people think that astrology is the Sun-sign columns found in every newspaper and online news media sites. Nothing could be further from the truth. That’s not astrology, that’s entertainment, which is what’s often stated in the fine print beneath astrology columns. Unfortunately, Sun-sign columns are one of the most persistently misleading representations of astrology. “
(Dorothy Oja: “What Astrology is and isn’t”)