You copied the Photos Library to the external drive, and then opened it again in Photos?
Where are you looking for the titles? Below the thumbnails of the photos or in the title field in the info of the photo?
Or are you looking inside the library package of the Photos Library?
Which system version is installed on the Mac?
The handling of the titles of the photos is depending on the system version. Some versions of photos are using the filenames of the photos as default titles, some don't.
- Photos 1 to Photos 3 did not use the filenames at all as titles.
- Photos 4 on Mojave did show the filename as the default title below the thumbnails and did sort the images by the filename when sorting by title.
- Photos 5 to 7 are also showing the filename as a default title, but do no longer sort by the filename, if the photo does not have a title.
We will only see the titles below the thumbnails, if we enable the option "View > Metadata > Title" in the View menu, and if we click the "Aspect" button to the left of the zoom slider in the toolbar, see: How to view the titles or filenames below the thumbnails in Photos 5.0 - Apple Community
How to switch between the tiles and the correct aspect ratio to see the thumbnails without cropping:

How to enable the titles below the thumbnails in the All Photos view and the albums:
