REST API needs an endpoint that allows the currently logged in user to change their password or other account profile information (e.g. name, telephone, language).
Likely, this endpoint should be off of "/api/authn/" path alongside the existing "/status", "/login" and "/logout" endpoints.
The functionality to actually PATCH individual EPerson objects has already been implemented (for Administrators only) off the /epersons/ endpoint at: https://github.com/DSpace/DSpace/blob/master/dspace-spring-rest/src/main/java/org/dspace/app/rest/repository/EPersonRestRepository.java#L193
So, likely, we just need a similar method which allows users to PATCH their own account information.