According to the band's website: "The name "Trans-Siberian Orchestra" was the brainchild of lyricist and composer Paul O'Neill. Paul envisioned the band as a musical train journeying across the world, uniting cultures, and spreading holiday joy. The "Siberian" part of the name alludes to the wintertime theme as the train would be filled with musicians performing holiday classics from around the globe. The "Trans" part refers not only to the orchestra's international journey, but also to its ability to transcend musical boundaries."
This is likely the fictionalized origin of the band's name, however, other sources credit the name being derived from the Trans-Siberian Railway, which is the longest railway line in the world. The railway passes through eight time zones and connects Moscow with Vladivostok. The Trans-Siberian Railway is often used as a symbol of the vastness and diversity of Russia, and it is possible that the band's name is a reference to this.