Upvote:1
Did you get some money from your university to do the PhD? In that case write your current university. Else write "not employed".
Write the truth. Do not overthink about the best answer you can give. They will eventually ask.
You come fresh from university, so it is ok not to have a previous job. This is also an advantage, which differentiate you from other visa (specialized worker, but this is especially true with other kind of visa).