Kom Abu Billo is a tell located near the village of Terrana el-Aguz, at the limits of the Libyan desert, 110 km south east of Alexandria. This site has issued numerous tombs of the 3rd and 4th century BC designating the city of Terenuthis, seat of a bishop during the Roman period. By the 1950s, Griffith recognized a temple of Hathor of Mefkat into scattered blocks of the Ptolemaic period. It is for this reason that the name of Mefkat is also associated with this location.
A stele found near the Lake Maryut dated between the 11th century and the 8th century BC, evokes a land donation to Hathor of Térénouthis by a Libyan leader. This confirms the existence of the site, with the name "Terenuthis" before the Ptolemaic period.
The IFAO launched in 2014 a research program on the extent of this ancient city. The necropolis shows a probable continuous occupation since the Old Kingdom:
As regards the former names of this site, the Terenuthis designation is confirmed by the Coptic use of "Terenuti" at the beginning of our era, which itself is at the origin of contemporary name "Tarrana".
It is possible that this name comes from "Ta Rennouti" meaning "Land of the goddess Renenutet", but not from "Per-Hathor-Nebet-Mefket" which is the city of "Pihattihurunpiki" mentioned by Ashurbanipal in the 7th century BC
Also, the name "Mefkat" does not seem a good one to me, because this appears only as attribute of Hathor, and it also means "Turquoise".
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My notes of veracity :
Kom Abu Billo, or Kôm Abou Billou, is the former Terenuthis: 5/5
Kom Abu Billo, or Kôm Abou Billou, is the former Mefkat: 2/5