Well, you can always do what my parents did and come up with a different nn right off the bat. My name is [name]Katharine[/name], but my dad hated the name [name]Kathy[/name]. So, he insisted that they only ever call me [name]Katie[/name] so that no one would ever call me [name]Kathy[/name]. However, that had poor implications as well. Since they only ever called me [name]Katie[/name] and only ever introduced me with that name, they might as well have named me [name]Katie[/name] and not [name]Katharine[/name]. I, of course, have never liked [name]Katie[/name] and it took me years to get people to call me [name]Katharine[/name] (family and childhood firends still won’t though). So, I don’t know that this would be my recommendation, but it is an option.
With my daughter, we introduce her with her fn and also our chosen nn. So, that could be an option similar to what my parents did and the other suggestions of kindly saying that she does not go by “[name]Mary[/name].” It gives other people an option of a nn, but one you would be okay with.
Of course, think about how much work it might be to stop the nn and then determine if the name is worth it to you. And don’t forget that your daughter may decide that she wants to be a “[name]Mary[/name].” If she does, then you probably will never stop that nn.