Here is the commentary from the Aquinas Study Bible
13:16-18 The False Prophet will cause many people from every class and status to receive the mark of the beast, and without it no one can buy or sell anything. The infamous number 666 is the number of the name of the Antichrist. Most languages has a number value for every letter in their alphabet, and there are numerous ways to reckon the number six hundred and sixty-six, so much so that it would be very timely to cover all the possibilities. For anyone who is interested in a resource that covers a lot of the calculations, I recommend the book “The Contributions of British writers between 1516 and 1830 to the Interpretation of Revelation 13:16-18”, especially chapter 8.
Perhaps the reckoning of the number really depends on what language St. John had in mind, whether he meant to reckon it from the Greek language in which he probably originally wrote the book of Revelation in, or whether he had Aramaic or Hebrew in mind. And since Scripture is inspired by God, it could very well be possible that the number is to be reckoned in a language at the time of the Antichrist and not a language from the time St. John wrote the Revelation. Perhaps this number is meant to be fully revealed at the time when it will be more beneficial to Christians to know its meaning.
As for me I favor the Greek word αρνουμε/ARNOUME, which means “I am denying.” It is orthographically identical with ARNOUMAI. E and AI are pronounced the same way in this era. This word appears to have first been suggested by St. Hippolytus (170-236AD) in his treatise On the End of the World, and then later suggested by Primasius around 550AD. The word has the numerical value of six hundred and sixty-six and is calculated as such…
A= 1 R= 100 N= 50 O= 70 U= 400 M= 40 E= 5 Total 666
Just as the sealing of the 144,000 on the forehead is not a literal mark, so the mark of the beast will not be a literal mark on the right hand or forehead, but the right hand is to be understood as the works of the hands and the forehead is to be understood as the confession of faith. I think the key to understanding this more fully is when St. John tells us in his epistle, “By this you know the Spirit of God: every spirit which confesses that Jesus Christ has come in the flesh is of God, 3 and every spirit which does not confess Jesus is not of God. This is the spirit of antichrist, of which you heard that it was coming, and now it is in the world already (1 Jn 4:2-3).” The mark of the beast is not meant to be understood as the proper name of the Antichrist, but it is concerning the “spirit of Antichrist”, which means to deny/ARNOUME Christ. The mark of the beast is already in the world because people receive it by denying Christ. This mark has always been around, but in the Great Tribulation the denial of Christ will be required in order to buy or sell, which will be a test for Christians who will be faced with the dilemma of either denying Christ in order to the get bare necessities, or to confess Him and face serious financial times as well as heavy persecution.
Here are some other calculations…
In Greek: Teitan, which τ three hundred, ε five, ι ten, τ three hundred, α one, ν fifty,— which taken together become six hundred and sixty-six. (St. Victorinus)
In Latin: DICLUX, which letters are reckoned in this manner: since D figures five hundred, I one, C a hundred, L fifty, V five, X ten,— which by the reckoning up of the letters makes similarly six hundred and sixty-six. (St. Victorinus)
In Hebrew: Nero Caesar (or Caesar Nero) was NRWN QSR.
St. Thomas Aquinas Sum Theo 3.63.3 said,"The ‘character of the beast’ may be understood by opposition, to mean either the obstinate malice for which some are assigned to eternal punishment, or the profession of an unlawful form of worship.