If you're using JMP 12 or later you can use Cols -> Utilities -> Text to Columns.
If you're using JMP 11 or earlier you can get the add-in, Text to Columns, Version 2, which does the same thing as the now, built-in function.
If you want to do this by hand, either with JSL or the Formula Editor, you'll find the Word() function handy, as described by thechadd
Last Name: Word( 1, :Name, ", " )
First Name: Word( 2, :Name, ", " )