From my admittedly uneducated viewpoint, it would seem to be fairly easy to step onto a ship as one person, and step off as another. Or even easier, to move to a new town and begin identifying themselves by a new name. Was it that easy? Was this common?
On the other side of things, for people being sought, what methods were used to track down someone who had attempted to disappear?
hi! there's a section in the FAQ* that deals with identity. There are two posts that discuss fugitives specifically, and it's likely that some of the other threads do as well
*see the popular questions link on the sidebar or the wiki tab above
Slightly later than your time period, but I'm currently reading King Leopold's Ghost, and it has a chapter dedicated to the 19th century British adventurer Henry Morton Stanley, and how he changed his name and identity as a boy when he arrived in America, and changed his life's story several times after that. I know speculation isn't allowed in the subreddit, but the fact this was happening well in to the 1800's strongly suggests it was relatively easy at least through that point.