Thank you! That shouldn't change the URL. If URLs are changing after making updates to reports, then you might want to reach out to Tech Support for further diagnosis. The way I usually share reports with people directly is by going to the top-right hand menu and selecting "Copy Link" to get a persistent URL like this:
https://my-viya-server.com/links/resources/report?uri=%2Freports%2Freports%2F7a18e812-aa3b-43d5-bf31-fbabd21290eb
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