A word or term for: "in another person's body"

The dreams could be wishful thinking, unconsciously you may be seeking to live a different life, to be someone else.

It could also be a signal that you are living a period of great stress, the dreams do not mean you physically abandoned your body and entered into somebody else's.

But depending on your personal beliefs there are a couple of expressions that interpret this type out-of-body experience (OBE)

channeling
The other incarnation of non-physical mediumship is a form of channeling in which the channeler goes into a trance, or "leaves their body", allowing a spiritual entity to borrow their body, who then talks through them. When in a trance the medium appears to come under the control of the spirit of a departed soul, sometimes entering into a cataleptic state, although modern channelers may not. Some channelers open the eyes when channeling, and remain able to walk and behave normally.

from Dictionary.com

incarnation
2. a living being embodying a deity or spirit.

From Merriam-Webster

out-of-body
relating to or involving a feeling of separation from one's body and of being able to view oneself and others from an external perspective.

Body-mind swaps are an oft used device in science fiction. One place it was used was in Star Trek (Original Series) in the last episode, Turnabout Intruder. A character used a Life-energy transfer machine to forcibly swap bodies with Captain Kirk.

In Star Trek: the Search for Spock, a Vulcan technique of Katra is used to transfer a body with two minds into a soulless body of another.

I do not believe they were dreams.

But they were dreams. They are known as "lucid dreams": https://en.wikipedia.org/wiki/Lucid_dream. They are not harmful but if you are worried, seek medical advice.