The most usual spelling is �moniker'. There is no certainty as to the origin of the word, but here are two possible sources. The first is Shelta, a secret jargon language used by Irish and other itinerants in Britain in the 19th century. It was rather like Pig Latin, in that it exchanged the letters and sounds of its words, though most of these were from Gaelic originally, to confuse non-speakers. In that lingo, �name' was �munnik', a typically distorted version of the proper Irish word. It's easy to see how that might have become �moniker'.
The second possibility is that it is a corruption based on the word �monk'. As early as the 1700s, �monkery' referred not just to the state of being of actual monks but also to the state of being of tramps. These �gentlemen of the road' apparently referred to themselves as being �in the monkery', almost as if their lifestyle was a religious calling! In addition, when someone became a monk, he would generally take a new name to indicate his new status. So that could be the necessary name-connection.
It seems, therefore, that whichever of these sources you consider, moniker possibly originated in the language of tramps. However, there is no firm evidence that either is the actual source.