We recommend at least having them in your bedroom with you in the beginning in either a dog bed or crate. Having your puppy in your bedroom with you will make them feel more reassured. It's normal for a puppy to need time and training to feel comfortable sleeping on their own through the night.
Puppies can learn their names quickly (most can pick it up within 1-3 days!) but generally, you'll want to practice using their name throughout their training sessions in order to ensure they respond consistently to their given name when said out loud. Save the nicknames for later so you don't confuse your pup!