Your question gets at an important problem that the field has been struggling with, well since always. If these are the "Middle Ages" or the "Dark Ages" they clearly have to be contrasted with something. Middle Ages implies a beginning and continuation, usually "Classical" (or Ancient) and then "Modern". "Dark Ages" implies that the light has gone out, therefore the light had to come from somewhere, and presumably be recreated. But these divisions are a legacy of what essentially amounts to angsty poets complaining that they were born in the wrong century, looking at you Petrarch. The long and short is that Petrarch decided his own time period, the 14th century, was a degraded and regressive time in history from the lofty heights of Classical Rome. He got the ball rolling on this and much of western civilization in the following centuries has decided to more or less agree with him.

So what would be a better term/way to phrase this time period? First there's the issue of even determining when the Middle Ages/Dark Ages were. I personally am rather traditionally inclined and am content to roll with 467-1453, or 500-1500 if you want nice even numbers, but other historians I've talked with also use the Rise of Islam in the 600's as a starting point or the acceptance of Christianity as the official religion in the Roman Empire and go until the Council of Trent in the mid 1500's, or the Reformation, or the Columbian Exchange. Each of these can have a case made for it. You can then subdivide ad-nauseum. You've got the Early Middle Ages, the High Middle Ages, the Crusading Period, the Viking Age, and so on. These periods often can even overlap with each other. However few of these would really reach a broader audience and that's fine, sadly not everyone can be an expert in Medieval history.

Really, this depends a great deal on context and audience. A lay, non-expert, audience probably would use Dark Ages, Middle Ages, and Medieval interchangeably and I wouldn't get flustered about it, we all start somewhere. I personally usually opt for Medieval Period/History over the Dark Ages or Middle Ages as I think it sounds slightly less pejorative (even though it means, well the Middle Ages). Historians in other fields might also continue to use this terminology. However for people within the field itself, it can get fairly nitpicky.