It is possible that the child only knows certain letters and those letters might be that classmates name, but not their own. My son is 5 and he still doesn't recognize all the letters, and is trying to learn how to read at school. I thought they needed to learn the letters first with sounds before they could read, but he is showing me different even though he is having a hard time.
Yes. When my children were becoming reading ready, they could identify that a letter belonged in a my name, their name, friends name, pizza hut, burger king, toys r us, etc. but did not know what to call the letter. They also could read some words without knowing what the letters were, such as things that they saw or liked like 'exit' signs, 'stop' signs, 'pizza', 'taco bell', flip through a magazine at the ads, you will be surprised at what they can read.
Start practicing letter recognition, children develop at different paces but all go through the same patterns eventually, but before children begin Kindergarten they should recognize all letters and order them in the alphabet. Numbers should also be familiar 1-20. I've included links to sites with worksheets and games that will help you teach your child. Flash cards and abc puzzles are good to use too. Starfall is a child friendly site, that they can use by themselves that teaches letters and sounds. It is important that they learn the sound the letter makes as well as the letter, so practice that also. Remember to read to your child. This will help too.