Windows still does store filenames in 8:3 format!
Drop into DOS and type "dir /-n" and it will show them. It used to store in 8:3 format and the long filename was in a system hidden file. It might be the other way around in newer filesystems but it still stores them somewhere!
If the 'destination path' is too long with long filenames, it might be a 256 character limit on the short filenames, so renaming them won't necessarily work as they may still be 8:3 - i.e. the same length!
Limits vary on Operating Systems so what may be fine on Windows is not fine on Linux (e.g. one is case sensitive, one isn't). It can also vary on filesystems.
If this is a backup you are doing to an external hard drive, many of them are formatted in FAT32 format. This format is old but works with most systems straight out of the box so it is commonly done for convenience. Reformatting it to NTFS or other filesystem may help. For example, FAT32 cannot store files larger than 4GB but NTFS can, so if there are large files the hard drive will fail to store the file from the factory but a simple reformat will solve it.
Your website on the other hand, some recent versions of Internet Exploder doesn't like links longer than 255 characters, including the http:// and parameters. You might need to consider this.