This mixed breed isn't common enough that it has its own unique nickname, but we can give it one right now: The Bull-Shep! Like their English Bulldog counterparts, the Bull-Shep is a very smart and tough but can be quite stubborn and difficult at times. Care should be taken to ensure your Bull-Shep is well-trained, which means that they may not be the best option for first-time dog owners that don't have experience training such a dog.
With the obstinate demeanor of the English Bulldog, and the loyal and protective nature of the German Shepherd, your Bull-Shep should be well-socialized around other dogs and humans. Both the German Shepherd and the English Bulldog can grow to be quite heavy, so daily exercise is of the utmost importance to maintain your Bull-Shep at a healthy weight.