Some interpret this Pasuk to mean that although he was the same king he was afraid of insurrection from the Jews. He was new because he became a tyrant. The Ibn Ezra says that he was himself a king who had usurped power for himself. He was from another country. A servant like Yosef who served the overthrown king would certainly not know Yosef. Some inventive Archaeologists have said that they have found out the name and time of this foreign king.
The Midrash has a different approach to this Pasuk. It implies that Paroh, whether he was the same or another, was an ingrate. Yosef and the Jews had helped build Egypt into a massive world power. Paroh felt comfortable that he did not need assistance.
The Midrash says: (from Torah Shelemah)
Why did the Torah punish ingrates? Because it is the same as denying G-d's existence. A person who denies the existence of G-d is an ingrate. A person who is ungrateful for his friends favor tomorrow will deny G-d's goodness to him. This is what we see in Paroh who did not Know Yosef. Until this point all of Egypt knew about his goodness. Paroh really knew Yosef but refused to recognize the goodness which he had done. His was ungrateful for Joseph's goodness. In the end he denied G-d's goodness as the Pasuk says "I (Paroh) did not know Yoseph."From here you see that Ungrateful people come to deny G-d's existence.
When I lived in Israel I had a job through my Yeshivah to assist American Tourists make Bar-Mitzvahs at the Kotel. This was done as a free service from the Yeshivah. I came in contact with two kinds of people. The first were ones which I assisted were great. They called me to tell me exactly what they needed me to do. I would make just a couple of phone calls and they would not stop thanking me.
A second type of person were the types who called me fifty times and changed their plans 60. After I bent over backwards for them they would yell at me how I destroyed their son's Bar-Mitzvah. Inevitably, I did much more work for these people then for the ones who I made only a few phone calls.
At home we see this all the time.
We should always be thankful to people for anything even if it small.