Actually that's one thing I don't understand about that song. The song automatically assumes you already know each of the reindeer. Aside from Rudolph I seriously don't know any of the reindeer. Can someone explain that to me?
The other reindeer were named in "A Visit from St. Nicholas," also known as "The Night Before Christmas" which was much more popular when the Rudolph song was written. Nowadays Rudolph is the only song about the reindeer anyone knows which which, ironically, makes the first verse very confusing.
Dasher! Cuz he could be 'dashing through snow in a one horse open sleigh, through the fields he goes, laughing all the way! Ohhhhh! Jingle bells jingle bells! Jingle all the way!' totally goes with the song