Hi @alexsina,
if an image is attached to a post (both standard and custom post), Phoenix Media Rename will update the post content to correct the image name and use the new one.
It is possible that some plugins are not compatible with Phoenix Media Rename because they use non-standard folder o database tables, if you run in this type of problem report me the issue and the list of active plugins are you using, I will fix Phoenix Media Rename compatibility or contact the other plugin support to ask them to fix on their side (sometimes is not possible to resolve on my side).
If you don’t want do risk a broken post, you can safely test the procedure:
1) create a new page
2) add a new image and mount it in the new page
3) save the page and close the editor
4) rename the image using Phoenix Media Rename
5) check if the page has been updated
Feel free to ask for further information.
C.