Medinet El-Fayum is often simply referred to as "Fayum". Near this town are the ruins of "kiman Faris."
During 1877-1878, the tell was used as raw material to supply limestone to farmland (sebakh). At this occasion, many papyri were found and bought by private collectors. Most are correspondences of the Roman period who had a cavalery garnison. They show that the city was called Arsinoe. This name comes from a queen of Ptolemy II, and can not be before this reign.
On this old site, the hardest materials, least usable, ie the statues or stones, are left behind and are the subject renovations.
The name "Fayum" is a deformation of the Coptic "Phiom" which itself comes from Pa-yom which means "Lake" during the New Egyptian Empire. For example, we find that description of a donation of Ramses III is worded as follows: "People to whom he gave, in the Temple of Sobek of Shedet, Horus, who dwells Pa-yom". It was deduced that the Temple of Sobek of Shedet was in this region.
The term "Sobek Shedet" or "Skedet" is a classic writing on the statuettes discovered at Kinan Faris. Several granite columns of the Middle Kingdom mention: "Sobek of Shedet, Horus who lives in Shedet". At Soknopaiou Nesos further north of Fayum, it is Sobek, Lord of the Lake, Sobek-Neb-Payou, giving Soknepaiou. To Tebtynis, next to the present village of Tell Umm el-Baragat in southeastern Fayum, he is worshiped under the heading Sobek, Lord of Tynis, hence the Greek name Soknebtynis.
It is these elements that lead to the conclusion that Shedet was the former name of the ruins of Kinan Faris before Arsinoe.
It is probably this city which Herodotus calls "Crocodilopolis" when he introduced his description of the Egyptian labyrinth, seen with his eyes, above the lake Moeris. A temple was erected in honor of the god where was kept a crocodile named Petsuchos, "son of Sobek" in a pond surrounded by a sandy beach.
But, there is a large number of Shrine of Sobek in Fayum, nothing is certain. Especially since it is admitted that there was in antiquity a water level in the lake more higher than now, as it is possible that Kinan Faris was underwater.
Here is a map made with Greco-Roman names found in the abundant papyrus of this region:
For French language, click here.
My notes of veracity :
At the beginning of our era, Arsinoe was the name of the city represented by the ruins of Kinan Faris: 5/5
In the 2nd millennium BC, Shedet was the name of the city represented by the ruins of Kinan Faris: 2,5/5
The Greek name of the city represented by Kinan Faris was Crocodilopolis: 2.5 / 5