As already noted by other contributors to this question, the Greek word means to figure up (to tally) or to figure out (to resolve). In colloquial English, we can say "to add up", which captures the full nuance of the meaning in Greek.
When we "add up" the Old Covenant, we see that the law is written on the mind and heart. The phylacteries (containing Torah) were placed on the forehead and the right hand (compare Ex 13:16 with both Deut 6:6, Deut 6:8, and Deut 11:18), because in the Hebrew Bible it was the right hand that was an extension of the human heart (Is 44:20). Identification with this Covenant therefore was a condition of participation in the visible theocratic kingdom of God. When we "add up" the New Covenant, we see that the law is written on the mind and heart (Heb 8:8-12). Identification with this Covenant therefore is a condition of participation in the invisible kingdom of Christ. When we "add up" the covenant of the beast (pseudo Moses/Messiah), we see that the law is written on the forehead and right hand (Rev 13:16-17). Identification with this Covenant will therefore be a condition of participation in the kingdom of the beast ("to buy and to sell") -- it will be "the law" as such.
The numerical value of the name of the beast here is the reference to his kingdom. For example, in 1 Kings 18:31, the number twelve (12) is correlated to the name of Israel. Thus Elijah in this verse explicitly equated Jacob (the man) with the name of Israel (the nation), which "add up" to twelve (12). The twelve (12) is not parallel with the man, but "add up" to the tribes (nation) associated with the man.
In like manner, in the Revelation the "beast" refers to the kingdom of the beast (Rev 13:1-2) or to the individual (Rev 13:3-4), who is its leader. Therefore in the Revelation, the "mark" of the beast refers to either the name of the person of the beast (Rev 13:17) or to the number of his name that corresponds to his kingdom (Rev 13:18). In other words, the "666" does not have reference to the name of the individual, but to the number of his name, which is his kingdom. (Please see the previous paragraph as to why.) So people are in Covenant with the "beast" are either in league with his direct politico-military control (under his name) and/or in league with the wider economic control of his kingdom (the number of the name). In either case, residents of the entire earth must have the "mark" (which can be either his name or the number of his name) in order to buy and to sell, which will be "the law."
In summary, the Old Covenant was led by the mediator Moses, whose "mark" was the Law (Torah), which was placed on the head and right hand (phylacteries). The New Covenant is led by the mediator Jesus, whose "mark" is the Law of Christ written on our conscience/minds and hearts (Rom 2:13-16 compared to 2 Cor 3:3). And of course the psuedo Moses/Messiah will be the mediator of his own Covenant with the world. His "mark" will be his name, or the number of his name, placed on the forehead or right hand, which "mark" will be the Law of life and living on earth (thus one will not be able to buy or to sell otherwise).
Thus one can "add up" the meaning of the number of the name of the beast. Please note that per the original question, no discussion of the meaning of "666" (or "616") was part of this posting.