How to delete session cookie in Postman?
Manually deleting it in the chrome browser removes the cookie from Postman.
In your chrome browser go to chrome://settings/cookies
Find the cookie and delete it
Edit:
As per Max890 comment below (in my version of Google Chrome (ver 63)) this is now
chrome://settings/content/cookies
Then go to "See all cookies and site data"
Update for Google Chrome 79.0.3945.88
chrome://settings/siteData?search=cookies
Postman 4.0.5 has a feature named Manage Cookies located below the Send button which manages the cookies separately from Chrome it seems.
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.