This could probably be done more efficiently with a script, but here is an interactive approach that will work regardless of the number of names in the Before table's Name column.
Highlight the Name column and choose Cols > Utilities > Text to Columns.
In the delimiter box type a comma "," and click OK. This will give you two new columns, Name 1 and Name 2.
Now Tables > Stack. The Stack Columns are Name 1 and Name 2. For convenience make the Stacked Data Column be called Final Name. Make sure the Non-stacked columns are set to Keep All, and click OK.
The resulting table will have some blank cells in the Final Name column. Right-click on one of those cells and select Select Matching Cells. Now go to Rows > Delete Rows. You can then get rid of the original Name column and Label column, if you wish.