No, there's not one single mention of Moses within the Ancient Egyptian records known to us. Suspiciously "Moses" is a name of clear Egyptian origin though. msj (mesi) is an Egyptian verb that means to "give birth", it's often used in theophoric names (DHwtj-msjw (Thutmose), "Thot is born"; ra-msj-sw (Ramesses), "It is Ra, who has born him") and msj (Mesi) or msw (Mesu) is a common shortform for those kind of names. It is kind of puzzeling that the greatest of all Jewish figures in the Old Testament has a name of Egyptian origin (he also married a foreign priest's daughter which violates Jewish modesty), but the Egyptian sources do not speak of him once.

As your question for a "similar individual" - yes, they kind of do. We know of the presence of "Asiatics", probably prisoners of war at first, in Egypt in the late New Kingdom. At the end of the 19th Dynasty, when the state of the New Kingdom was already crumbeling, there are the intriguing figures of Bay and Irsu. Bay was supposedly already a person of high importance under Pharaoh Seti II. (1200-1194 BC), mentioned as a steward (wdpw) and royal scribe (zS njswt) in one Ostracon (CG 25766), furthermore described (in the same Ostracon) as a "stranger from the northern land" (qr nj pA tA mHj). Bay is not an Egyptian name, but according to one record from Assuan he wore an Egyptian name, too - Ramesses Khamenteru (ra-msj-sw-xa-m-nTrw). Bay continued to play an important role under Setis successor, Pharaoh Siptah (1194-1188 BC), still a child when crowned king, suffering from polio (he had an atrophied leg) and therefore under the regency of his stepmother, Tausret, who after his early death proclaimed herself queen (1188-1186 (?) BC). Bay seems to have been the éminence grise, who held most of the power in the shadow of the throne; several titles are attested to him (among them "chancellor of the entire land") and he is portayed in the same height as the Pharaoh in some depictions (which is really unusual for a commoner), he was even granted a grave vis-à-vis with the royal tomb (KV47), alongside Queen Tausret (KV13+14). In some inscriptions he claims to be the person who "established the king on the throne of his father" - a phrase normally reserved for the gods, highly unusal for a mortal, particulary a commoner and foreigner like Bay. At some point he seems to have fallen out of favor, because another Ostracon (IFAO 1864) seems to mention his execution, in the fifth year of Pharaoh Siptah; he was treated as a traitor subsequently and his grave was never used until it was upsurped by the 20th Dynasty. This account of his execution corresponds well with the fact that Bay is not mentioned after the fourth year of Pharaoh Siptah in any official records.

Papyrus Harris I contains a speech of Pharaoh Ramesses III. (1184-1153 BC), who after his father Setnakhte (1186-84 BC) had usurped power from Tausret and therefore founded the 20th Dynasty, attempted to stabilize the disrupted country. In this speech the Pharaoh renders an account of his good deeds for the country and mentions the disrupted state of the country before his and his father's reign.

The land of Egypt had fallen into confusion, every one was doing what he wished, there was no superior authority for many years which had priority over others. The land of Egypt was under the chief of nomes (districts), each was killing another out of ambition and jealousy of another coming after him. After some years Irsu, a Kharu (Syrian), amongst them as chief placed the whole country in subjection to him. One united his companions to drag things away, were treated the gods as if they were men, no sacrifices of offerings were made in their tempels.

Payprus Harris I, 75,3-6

This is a typical Egyptian description of the state of Chaos, were everything good is turned into evil, because of the absence of royal order. More interesting here is the mention of "Irsu", probably a polemical nickname ("one who made himself", a "self-made man", meaning an usurper), who gained enough power - even as a foreigner - to subjugate the whole country and allowed his men (probably other Asiatics) to do the horrible things described above. It has been suggested before that Bay-Ramses-Irsu is effectivly the same person (though it seems unlikely now, with the publication of IAFO 1864, which mentions Bays execution under Siptah, which means he would have been dead by the time Setnakhte arose to the throne).

A stela in Elephantine, one of the few records of Setnakhte's reign, describes how he fights off "Asiatics" (nn nj stty.w, "these Asiatics", it's not entirely clear which ethnicity the term stty.w is supposed to describe, probably a levantine people). The stela describes how these Asiatics plundered Egypt and looted gold and other precious metals, which they left behind when Setnakhte expelled them from the country. The stela is dated to the second year of Pharaoh Setnakhte's reign and not to his first and may indicate that conflicts lasted for a longer time period, preventing Setnakhte from uniting the country under his power. Obviously both accounts are linked, Asiatics, under the leadership of a certain Irsu, seem to have seized the moment and gained a position of high influence until they were expelled by Setnakhte. We do not know which role Queen Tausret played within these conflicts or if she was still alive at all at this point.

There are some striking similarities between the scarce Egyptian accounts and the story of both Joseph and Moses. Foreigners, "Asiatics", whereever they came from, rose to high power in Egypt and were subsequently expelled from the country. The story of the stela of Elephantine - the gold the Asiatic rebels left behind, when they fled - corresponds with Exodus 12:35-36, where the Hebrews are said to have acquired large amount of golds from the Egyptians. The Egyptian name of Bay, Ramesses, could be origin the of the name Moses.

The ultimate problem here is that we essentially know very little of Bay and Irsu, whoever they were - in fact, we do not even know with certainty if they were one person (seems unlikely though). The fact remains though, that towards the end of the New Kingdom foreigners, "Asiatics", could rose to high power and were obviously responsible for a lot of the trouble that shook the last days of the 19th Dynasty. It's highly unlikely that the tale of the Exodus and of Moses are entirely fictional myths, they most probably carry a kernel of truth, a faint image of a reality long passed by when it was written down, an image that may reflect the troubled days of the transition from the 19th to the 20th Dynasty in Ancient Egypt.