I am testing my API in Postman and am having trouble simulating a log out.
If I do a call to delete the session cookie,
As @markus said use the "Cookie Manager" and delete the cookie.
If you want to learn how to set destroy cookies in postman, You should check the Postman Echo service https://docs.postman-echo.com/
There you will find complete explanation on how to Set, Get and Delete those cookies.
Check it on : https://docs.postman-echo.com/#3de3b135-b3cc-3a68-ba27-b6d373e03c8c
Give it a Try.