You cannot customize the "URL" in the standard "Forgot Password" page. If you hover around the "info" icon, you will get to see the details as below:
The URL of the page. Editable only in custom standard pages.
If at all you want to customize the URL, you will need to:
- Create a new custom page. While creating the page (or even after it has been created), you will be able to provide any custom URL that you want to use. Something as below:
- Utilize Identity Component "Forgot Password" to utilize the OOTB password reset functionality
However, remember you will also need to override your standard Login page for this to make sure you provide the link to your new custom page.
Additional note: If you don't see Identity Components in your Org, you will need to reach out to Salesforce Support to enable that. There is some permission that they enable from back-end, and only then those components start showing up in the list.