The word "possessioner" is quite uncommon, and there are not many synonyms for it. One possible substitute could be "owner", which conveys a similar meaning of having control over an object or property. Another option is "holder", which implies a temporary or partial possession of something. "Custodian" could also be used to describe someone who is responsible for looking after a certain item or place. "Occupant" and "resident" both refer to people who possess a physical space or dwelling. Lastly, "keeper" can be used to denote someone who has care or control over a certain thing, such as a key or document.