Lightroom's image file management function is a database manager rather than an image file browser.
Database managers and browser differ significantly in how they work.
A further complication is that a LR catalog can only be accessed by 1 computer at a time.
Image files are not stored
in LR. LR only keeps track of where the files are on your computer memory (the memory path).
Consequently you must use LR to do any file renaming, moving, etc.
If you use your computers file management function to move or rename image files LR won't know those changes have been made.
With 2 computers if you move image files using your laptop, the LR that is installed on your desktop won't know where they got moved to.
LR does have a function that will go looking for moved files.
I highly recommend these 2 books:
The DAM Book: Digital Asset Management for Photographers
The Adobe Photoshop Lightroom 5 Book: The Complete Guide for Photographers
There are several approaches to keeping your 2 installations of LR in sync when using 2 computers: