The word פרעה seems to be a transcription of a Egyptian word. But there is some kind of (explanational) link to be found with the word פרעה in Exodus 32:25.
The Rambam links the word פרעה with the Yetzer HaRah.
Horav Eliyahu Eliezer Dessler, zl, remarks that this idea is implied by the name of Pharaoh. An allusion to the meaning of the name Pharaoh is to be found in the pasuk describing the sin of the Golden Calf: "Moshe saw that the nation was paruah, exposed, for Aharon praah, had uncovered them" (Shemos 32:25). Rashi interprets this: Paruah means exposed, for the nation's evil and shame was revealed. Thus, paruah/Pharaoh denotes a breaching of the parameters of the heart, a granting free rein and open license to the evil-inclination. This is Pharaoh. It is to this exposed, unabashed evil-inclination that the Rambam refers when he says that Pharaoh embodies the essence of the evil-inclination. Man's resistance to restriction and confinement lies at the root of all sin. No one wants to be told, - "No!"
In addressing the original question, Rav Miller cites the Malbim who underscores Pharaoh's reaction to the concrete display of Hashem's Omnipotence. He explains that the purpose of the first three plagues was to demonstrate that Ani Hashem, "I am G-d," the existence of Hashem's power. The second set of plagues was to demonstrate the concept of Divine Providence. Hashem is powerful, and He controls every aspect of this universe. Now, Pharaoh was threatened. He felt that he was the undisputed ruler of Egypt. No one else could undermine him, or claim this position. Pharaoh could not deal with this. His identity as supreme ruler was being challenged, restricting the extent of his total control over the freedom of others. The third group of plagues crumbled the last vestige of Pharaoh's imaginary power, for they attested, without any room for doubt, that Hashem was the Supreme Ruler and power. Each step in the process called the Ten Plagues presented further indication to Pharaoh, the individual who challenged any form of personal limitation, that his powers were truly restricted.
During this entire process, Pharaoh refused to acknowledge the fact that he was not in control, that he did not dominate. In the beginning, Pharaoh could still render his own decision, but in the third set of plagues, this, too, was taken from him. He was now completely confused. It was at this point that he was admonished, "How long will you refuse to be humbled before me?" You have already lost everything. Do you not see that you are not what you think you are? Your mind is no longer your own. You have lost your free choice. You have been censured for refusing to acknowledge your limitations and Hashem's Omnipotence.
Pharaoh's defiance, his virulent objection to the limitation of his own power, identified him as evil incarnate. The Ten Plagues taught him how wrong he was.
P.s. found a lot of commentaries based on wordplays: