Assuming the current buffer is a file open for edit, so :e does not display E32: No file name.
I would like to yank one or all of:
If you do :reg you will see the name of the current file in the % register. You can paste it with "%p, for example.
If, like me, you often switch to the 'alternate' buffer, it is very handy that its full path-and-file-name are put in the # register. You can paste it with "#p, for example.
Note (just in case this is behaviour specific to my setup): I am using VIM 7.4.52 on Ubuntu 14.04.4 LTS.