You would not lose any permanent will never lose a Permanent Character Title. Once these are unlocked they are assigned to your character forever. If the character title is a Temporary Character Title (eg. Globetrotter), you will only lose this if you no longer meet the criteria. There are many Character Titles that are not permanent though and you will change during a World Merge. For example, Highest Level, Highest Distance, Highest Magic, etc for a particular world.
In the example of Globetrotter this will not be lost during a World Merge but could lose those. be lost in a future update if you no longer meet the criteria.