When you're doing a media audition - either voiceover or on-camera, the introduction is called a slate. The slate is your name and sometimes your agency info, your contact info, or the name of the character or the project. Pay attention to the specific slate instructions and make sure you follow them.
But, if you're given no instructions about the slate or just told to 'slate your name' then this means say your first and last name at the beginning of the v/o track or do a brief greeting/intro with your name when they first roll camera at the on-camera audition 'hi, I'm Joe Actor'
Do this intro as yourself, rather than using the character voice in the voiceover or the given circumstances of the on-camera audition. And, it's your opportunity to introduce yourself to the client or director of the project. Usually, you're recording the voiceover audition in your home studio or with a sound engineer, or you're doing the on-camera audition with a casting agency's session runner, not the actual people who will be making the decisions about which actors will be involved in the project.
For voiceover, the intro is done. But for on-camera, there may be a few more steps. They may want to take a photo, zoom out so they can see your whole body, have you show profiles or do a 360, or show the fronts and backs of your hands.
If you're asked to show profiles, this means that you'll do a turn to both your left and right and show both sides of your face. If you're asked to do a 360, you'll turn in a circle so the camera can see you all the way around. Practice these with a friend and a camera so you can figure out how quickly you should move when doing these maneuvers.
Similar to the theater audition, the slate and the rest of the intro is your chance to show that you're both professional and personable. That you're going to be a good person to have on set - you're friendly, efficient and good at what you do.