In one of the snapshots I was able to search object names, but that seems to have not made it into 1.2.5? Or was it moved?
The development snapshots lead up to the next new feature release, Tiled 1.3. The latest snapshot is currently the Tiled 1.3 Beta, which includes the search filter for the Objects view.
In contrast, Tiled 1.2.5 was a patch release to fix a few issues that were discovered since Tiled 1.2.4. It does not introduce new features because it’s meant to be stable.