Your budgie is sleeping. Budgie's are really light sleepers so if you turn on the lights (or have the lights off) and peek in their cage they will know and will be alert to find out what's going on around them. They are very alert with any movement. It is normal. Just make sure he does get a good night sleep without any noise for at least 8 hours a day. Keets should sleep 10-12 hours a day, a chunk of it is done at night.
You don't have to repeat the desired word over and over, you can mix it in with other words and just say the desired word much more times than the other words just so it doesn't get tiring. Once he learns how to say his first word, it gets much easier for him to pick up other words.
If you want him to learn his name or your name just say it to him a lot.
Good luck and hope everything works out! Let us know how it goes!