It is uncertain exactly when the Picts came to Shetland, but it would seem that they were there by the Iron Age. It is thought that they spoke a Celtic language . Very few Pictish names remain in Shetland and it is disputed why this is so. Many of those that exist are disputed, but it has been suggested that the names Unst, Yell and Fetlar may be of Pictish origin. The Norse also named a few places after them, e.g. Pettester (Pictish Farm) in Unst, and Pettesdaal in central Mainland 
They were a pagan people, but appear to have been becoming Christian, or even completely Christianised by the time of the Vikings. Some of the items in the St Ninians Isle Treasure are of probable Pictish origin.
Their name appears in various different forms - Picti/Picts (from the Latin), Pecht, Pett etc. In Gaelic, they were known as "Cruithne", which may be related to "Pretani", a Latin name for the Brythonic or P-Celtic peoples.
The Latin name, "Picti", may refer to their being painted or tattooed. It is arguable whether they would have ever referred to themselves as such.