Hello SailorMama,
Welcome to Apple Support Communities!
We understand that you want to know if there is a better way of saving videos and pics that are sent to you so you can change the name of them instead of the Files app. We're happy to provide you with a suggestion.
You could save the videos and pictures to iCloud Drive instead of Files so that you can rename these files. Below is the article about iCloud drive.
iCloud Drive FAQ
If you decide to use iCloud Drive then this article will be helpful for renaming files and folders: Rename files and folders in iCloud Drive on iCloud.com
Let us know if you have any questions.
Thank you for using Apple Support Communities.
Take care!