You can bind these keys and the corresponding Action to the JTextArea or one of its parent JComponents. The How to Use Key Bindings page in the tutorial shows how to do this.
JTextArea has an insert method that may be useful for adding the name. Also, its superclass JTextComponent has handy methods for moving around in a JTextArea. You can find the JTextComponent methods that apply to JTextArea in the Methods inherited from class javax.swing.text.JTextComponent section of the JTextArea api.