Of course, you can always take a seam ripper and remove the monogram - which, when very carefully done, can easily be covered up with the new. But - a cute applique can turn a one of a kind outfit into something that can be worn again and again - even to be passed down a third time (if that's the case).
Note: This is true too for clothes you find on ebay or on consignment. Don't count it out because it has a monogram on it that doesn't match... let's find an applique in a coordinating fabric. It's cute AND you'll probably get the clothing for an inexpensive price since it's personalized.