You are not obligated to say that you are laid-off, but, at the same time, there is no stigma attached to it, either.
I've been laid-off many, many times over these many years.
Organizational Unit in the La Gov HCM system has a different use and definition and thus should not be confused with organizational unit as it is used for layoff or layoff avoidance purposes.
For further information regarding La Gov HCM terms, see Job Aids & Resources: Organizational Unit for Layoff vs La Gov HCM.
This chapter contains provisions for when an agency implements layoff avoidance measures or a reduction in force.