Are MLB baseballs marked to identify one correctly if it becomes a major event - such as a first home run for a rookie?

Yes, but they would not used marked balls for something like a rookie's first home run. MLB will use marked baseballs when an event can occur that would make the baseball a lot of money for a fan ... a collector's item. After Barry Bonds hit #755, every time he came to bat the ball boy would bring the home plate umpire a batch of baseballs.

Those balls were marked with a number. The home plate umpire kept track of the number of the ball in play so that when Bonds hit #756, there would be no confusion as to which fan had the correct ball.

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