panel: how to obtain the name of the uploaded file?

Question

While using param.Parameterized way of creating a Panel application, I am not able to obtain the name of the uploaded file. The minimal code is below, I am trying to figure out the solution for the update_name method:

import panel as pn
import param


class TestFile(param.Parameterized):
    file_upload = param.FileSelector()
    file_name = param.String()

    @param.depends("file_upload", watch=True)
    def update_name(self):
        ... # how?


test = TestFile()
app = pn.Row(pn.Param(test.param, widgets={"file_upload": {"type": pn.widgets.FileInput}}))

app.servable()

It seems that doing this would require creating the widget inside the class, since pn.widgets.FileInput does have a filename property. Is there a way to get the file name of the uploaded file without using pn.widgets?