The short answer is: "No, there is no evidence of this in historical records".
The word, 'pharaoh' [pr aA] is first attested in the First Dynasty, about 3150 BCE. It means 'great house', or 'palace'.
It wasn't used as a title by Egyptian kings until the reign of Thutmose III in the New Kingdom (his reign lasted from about 1479 to 1425 BCE). From this point, the title 'Pharaoh' becomes the norm for Egyptian rulers.
Interestingly, Thutmose's step-mother, Hatshepsut, who preceded him as ruler of Egypt, is often referred to as 'the female Pharaoh', by modern authors, but - as far as I'm aware - no contemporary text or inscription includes 'Pharaoh' among her titles.
Nimrod, on the other hand, is a figure mentioned in the Bible, but one who probably didn't actually exist as an historical figure. Even in the Bible, he is not an Egyptian king, but a king in Mesopotamia. As the Wikipedia article observes:
Attempts to match Nimrod with historically attested figures have failed. Nimrod may not represent any one personage known to history, and in reality is more likely a conflation of several real and fictional figures of Mesopotamian antiquity.
As for the story of Rikayon, a character supposedly mentioned in the Book of Jasher, that may be a question better asked on Biblical Hermeneutics:SE.
However, there are a number of translations of later versions of the text available online, such as this example of the Book of Jasher from a book written in from 1613, if you with to wish to follow up on the stories.