How may I find the date on which I changed the catalog anme in order to restore?
Renaming a LR Catalog .lrcat file shouldn't cause the problem you describe (? marks on photos). However, you also need to rename the associated Previews and Smart Previews .lrdata folders as outlined here:
It won't. Not renaming the previews and smart previews means that Lightroom will have to rebuild those. It will rebuild the previews automatically, so you still should not see this problem. A question mark on the folders means that Lightroom can't find the photos however (and so it won't be able to rebuild the previews either). You must have changed folder names too, or perhaps your photos are on a disk that has a different drive letter than before (if you use Windows).