When you click to save a video you will first be asked "Do you want to save this file". Click Yes.
On the next screen you will see two Fields. One for "File Name" and one for "Destination". Click the Up or Down arrow on the D-Pad on the left side of your PSP to highlight the "File Name" field and click X to Enter.
Type out the name that you want, including .mp4 at the end. When done, press the "Start" button on your PSP.
Click the Down arrow on the D-Pad on the left side of your PSP to highlight the "Save" option and click X.