Have you tried Add Category for ... ?

Result:

It's often easier to leave the data in the same table and just add/change names there. But if you need separate tables in the end just create a new table, select the cells you want from the data table, command-c to copy, click a cell the destination table, and command-v to paste.
Another way would be to use a Pivot Table to quickly set up separate tables.
Click in the data table and from the menu choose Organize > Create Pivot Table > On Current Sheet and set it up like this (just drag Table down into the Rows box and Name into the Values box):

The right-click (control click) a cell of the Pivot Table and choose 'Create Table for Data Source':

That gives you something like this:

Which you can quickly clean up into something like this:

SG