There's no single format that will accomplish what you want.

In fact, I'd recommend that you put your data in two cells.  And use Name and
Date as the header for those columns.  It may not look as nice, but you'll find
that you can do more things more easily with the data split this way.  (It may
look nicer than you think!)

If you really, really, really want (I wouldn't!), you could give each cell a
custom format.

You only type the date in the cell and have the formatting add the text you
want.

I put 6/16/2007 in A1 and gave it this custom format:
"Name: Jeff Willis"* "Date:" mm/dd/yyyy

The value in the cell is still the date.  But the cell's text (what it shows) is
what you want.

The asterisk in the custom format string means to use the next character as a
filler when the cell's column width is extended.

Please don't do this <vbg>.