Despite, only this year they will finally make the bald eagle the national bird. Which, I also learned that they are not official symbols until a President signs a document for them to be. It is just a recognized symbol but not official. (Just my opinion but why do they really need a bill for this? What changes would making anything like this official really do?)
Here is a list of other US symbols (article includes links to other countries of the world national symbols, some official, some not made official) if you are interested:
https://en.m.wikipedia.org/wiki/National_symbols_of_the_United_States
Countries have national animals, if you look on the list of other countries’ animals, you can see it is usually because they are the most common or most unique in some way.