Here is a song with all of Santa’s reindeer named. This song is written and designed to teach young children the names of Santa’s reindeer.
Here’s what I recommend doing. Assign nine different children a reindeer either in stuffed animal form or felt form or have nine children wear antlers and represent one of the nine different reindeer. Have a designated place for each child to go or to put their stuffed animal or felt reindeer as they hear the reindeer being named in the song. If you are concerned about including every child you could have a few double up per reindeer.
This activity works best for children who understand how to read or differentiate between each reindeer given to them. For year old children, kindergarten children and maybe older ones will understand it best.