Is this, by any chance, a project that's been imported from an older Eagle version? That seems to be the most common cause of such errors.
The fix, unfortunately, probably involves a text editor (on Windows I recommend Notepad++).
- Make a backup of your files first
- Open the .brd file in a text editor and go to line 3851. Around column 26 you should see name='' (two single quotes, probably).
- If you can work out what the item on that line should be called, then type that name between the quotes.
- Otherwise, type something like fix1 between them.
- Save the file and try opening it in Eagle again.
If it opens OK, locate the item you corrected and rename if necessary. You may well get consistency errors, and you'll need to fix the schematic to match. Sometimes, when you've fixed a missing name issue, the file still won't load because there's a similar problem on other lines, in which case fix each one the same way (use different names, obviously) and keep trying until it loads.
If it all goes horribly wrong, restore from your backup and try again (or upload it here - some kind soul may be willing to put the effort in and fix it for you).
