[knarf]

"Also known as The Holy Shroud" is used once in that link.

Following many but not all of the reference links provided led me to numerous references to The Shroud, but no Holy Shroud

[annalex]

no Holy Shroud

Really?

Using the Italian wiki article, link to which I posted in my #5, as a starting point, without any difficulty I find:

Cappella della Sacra Sindone
Indagine sulla Sacra Sindone

"Sindone.org - Sito ufficiale" ("official Shroud site") link leads to a site http://www.sindone.org/the_holy_shroud__english_ that has "Holy Shroud" right in the title, in three languages, including English, even though their Italian title is Santa Sindone (literally, "Saint Shroud") rather than "Sacra Sindone".

[annalex]

Matter of fact, a search on '"Holy Shroud" Turin' turns up plenty of English-language sites as well:

The Holy Shroud (of Turin)
The Holy Shroud of Turin
Museo della Sindone (The Holy Shroud Museum)

It is, in short, a well-established usage. Generally, we refer to relics of any kind using the adjective "holy": just google "holy relics" as a single item.