25 is the age in a lot of jurisdictions in North America when car rental companies will rent you a car.  In some places it's 21 where they're forced to by law, but for the most part it's 25.  I believe the reason I was given several years ago was it had something to do with insurance.

So, leasing arrangements may be similar.  This doesn't sound like an outright giveaway, though - they can sell you a car outright if you're an adult (21).

I would have just said yes I'm between 25 and 76, because my father has the same name as me so he could just claim the winnings.

Odds are, they didn't want to give the car away so they picked your name because it was under the age limit of the contest, or only told you about it.  If I were you, I'd find out what contest it was, call her back and find out the rules, then I'd get very very mean if they didn't tell you the right answers.