The name Trellium is used by readers to reference the unknown metal referenced in both Shadows of Self and Bands of Mourning. It gains this name in reference to the presumed god/shard currently known as Trell on Scadrial. It follows the trend of other God metals in using the actual name of the shard bearer plus 'ium'. Ati + ium = Atium for Ruin and Leras + ium = Lerasium for Preservation. It does not yet have an official name and is referred to in the books simply as an "unknown metal."
This unknown metal is used for the Hemalurgic spikes that keep the user hidden from Harmony. First seen with Paalm in Shadows of Self, they are also presumably seen in Bands of Mourning used by the Set. It is possible that this is the metal referred to by Miles Hundredlives in his final words as "the final metal."
It is unknown what this metal's Allomantic or Feruchemical powers would be or if it has any at all but presumably its hemalurgic ability is similar to that of Atium, allowing the transfer of any ability with somewhat variable success depending on the binding point. It could also be assumed that, like Atium, any ability provided through its spikes would be fueled by its respective shard, Trell, rather than Preservation.
It is unknown what Shard Trell holds if indeed he is a Shard. One possibility would be that Trell is Odium. To our knowledge, Odium is currently bound to Braize in Greater Roshar the same solar system as Roshar of the Stormlight Archive leading one to believe that it may be another shard. However, since the second era of Mistborn takes place after the first five books of the Stormlight Archive and possibly even after the second five books, it is entirely possible that Odium is no longer bound during the second era of Mistborn. If Trell indeed is Odium, Trellium would more appropriately referred to as Raysium.