What you've asked for is not easily done in a formula (that I can come up with anyway). It's relatively easy to do this interactively by using Tables->Sort to sort the table into a new table and then copy and paste the column of interest back into the original table.
However the question raises some interest about what you're really trying to do.
Generally speaking, a row of a data table represents a collection of values for a single entity – an individual student in your simple example – and each row is unrelated to other rows. I'm not sure how this new column – of Names in your example – would be useful in an analysis since the new column is only meaningful in the context of it's order.
Can you explain a little bit more of how you'd use this new column?
An example to hopefully clarify: if I had a table with two rows: Name and age, how would I create a third row that displays the names sorted from oldest to youngest?
PS: you seem to have confused rows and columns in your example. I'm assuming that you really meant a table with two columns and that you wanted to create a third column as your original question states. If I'm mistaken and you really meant rows, please let us know.
-Jeff