"The Information Age" is a quite correct term. As for your question about what age are we currently in, well, I can't answer that. The answer could be almost anything that you would like it to be, and it probably depends on what your interests are. Some people might say that we are in more than one age. Sometimes, what age we are in isn't obvious until it has passed by, and we can look back. So, pick your current age, whatever it might be!