Of the three names, Atropos is the only one that describes a disposition rather than a craft. Clotho spins and Lachesis allots, both ordinary working verbs. Atropos is a-tropos, not turnable, from the same root that gives the Greek words for turning, twisting and being deflected. The name is a refusal, and it belongs to a family of Greek divine names that state a limit: what she is is the fact that persuasion does not work.
That is a stronger claim than it looks. Greek religion is built around approaching a power and asking, and most of the divine figures a Greek would name can in principle be moved by prayer, sacrifice or an argument put well. The Moirai as a group are marginal in public cult for exactly this reason, and Atropos concentrates the difficulty. There is no useful transaction to conduct with her. What art gives her, a pair of shears, is a household tool, and the ordinariness is part of the point: the end of a life is figured as a small, decisive, entirely unremarkable domestic action.
Later art added other attributes, a sundial or a scroll among them, which move her from cutting toward measuring time or reading out what has been recorded. The shears remained the recognisable sign, and the name kept its meaning well enough that it passed into Greek prose as an ordinary adjective for something that will not be diverted.