When the "Auto-name Files" option is enabled, you can add a time to the file name by checking on the "Include Time" option.
Auto-name Settings - Include Time
The time format can be selected to the right of the option, and available formats include:
•12 Hour-Minute-Second-Millisecond-AM/PM (default)
•12 Hour Only-AM/PM
•24 Hour Minute-Second-Millisecond
•24 Hour Only
The "Sample File Name" listed at the bottom of the window is updated to show the resulting file name based on the options selected. This option can be combined with any of the other auto-name options.