How to replace booze in eggnog?
The easiest way is rum or brandy extract. The flavor is milder, but satisfactory enough. (Rum extract is far easier to find than brandy extract.)

Most brands still have some alcohol (significantly less than the real deal, but still present), so it's important to consider whether you're just avoiding the intoxicating effects or trying to completely eliminate the alcohol (e.g. for medical or religious reasons). If work rules mean it needs to be completely alcohol-free, you'll need to get more creative.

A side note inspired by a comment asking if eliminating alcohol increases Salmonella risk: Alcohol isn't guaranteed to kill harmful bacteria, so nog should either use pasteurized eggs or be (lightly) cooked for food safety... regardless of how much booze is or is not in your recipe.