Good question. The concept of the ‘artist’ is very much a medieval phenomenon, from about the 13th century onwards. Before then, art and craft, whether painting or bricklaying, were considered jobs to be done by people whose job it was to do them, rather than individual expressions of creativity. Of course, the attribution of artistic masterpiece is something of a subjective opinion, but a quick review of almost all the pre-medieval, and indeed a great many medieval art-works, will show that we have no idea who made, painted, sculpted or built them. In more modern times, we have begun to recognise individual talent in a way that was never done before, and attributed some medieval work to “the master of…” this or that, without knowing his name. Sometimes, research into archives will reveal an individual name (usually in connection with having been paid for a job), but more often than not, the earlier the artwork, the more anonymous the artist.
Furthermore, the Shroud was not intended, in my view, as a ‘signature’ artwork. It was a functional artefact with a job to do, and as such, almost any of the known artists from the trecento could have produced it. They could not have known of its ‘negative’ effect, of course, which is an accidental outcome of the skill of their original design, which was to produce an image that might have been produced by a recently traumatised corpse.
If I was given the research grant hypothesised by nooooby above, some of it would certainly be diverted into the study of the Italian artists of Siena and Florence of the time, some of whom also spent some time in Avignon with the exiled popes, with a view to characterising their individual styles with that of the image on the Shroud. They could well have been known to Bishop of Troyes Henri de Poitiers, who allegedly, as we know, knew who had created the Shroud.