Stream was created on Demons Run by Madame Kovarian, along with six other clones. After the Eleventh Doctor raided Demons Run, Stream escaped on a ship with the other six clones. As part of his religious cult, Lake convinced them to die multiple times on Terminus Prime so he could covertly study regeneration and find out how long he was able to live. (AUDIO: The Lady in the Lake)
Behind the scenes
Like all of their siblings, Stream's name is a reference to water, with their name coming from the word steam, which is a body of water with surface water flowing within the bed and banks of a channel.