Update renaming-an-organization.md (#53024)

Co-authored-by: Sam Browning <106113886+sabrowning1@users.noreply.github.com>

content/organizations/managing-organization-settings/deleting-an-organization-account.md

@@ -27,12 +27,6 @@ shortTitle: Delete organization
 {% endif %}
 Deleting your organization account removes all repositories, forks of private repositories, wikis, issues, pull requests, and project or organization pages. {% ifversion fpt or ghec %}Your billing will end and, after 90 days, the organization name becomes available for use on a new user or organization account.
 
-{% tip %}
-
-**Tip**: If you rename an organization, you can create a new organization with the same name immediately. For more information, see "[AUTOTITLE](/organizations/managing-organization-settings/renaming-an-organization)."
-
-{% endtip %}
-
 {% endif %}
 
 {% ifversion fpt or ghec %}

content/organizations/managing-organization-settings/renaming-an-organization.md

@@ -22,7 +22,7 @@ topics:
 
 ## What happens when I change my organization's name?
 
-After changing your organization's name, your old organization name becomes available for someone else to claim. When you change your organization's name, most references to your repositories under the old organization name automatically change to the new name. However, some links to your profile won't automatically redirect.
+After changing your organization's name, your previous organization name will be unavailable for anyone to claim for 90 days. When you change your organization's name, most references to your repositories under the previous organization name automatically change to the new name. However, some links to your profile won't automatically redirect.
 
 ### Changes that occur automatically