The biggest problem with beagles is probably their love of food and they love to explore. Beagles love to sniff and explore this could get them into trouble so extra precautions are needed to keep them out of trouble so they don't get away from you. Also Beagles love to eat and eat and eat some more. For the health of an animal there is no real guarantees.
Reputable breeders can eliminate the possibility of many problems on the list.
Sometimes its best to wait and see what personality your dog has this can help when naming. It should be a name easy for you to use frequently because beagles are so stubborn you will be using it quite a bit.