The answer to this question can go in two directions:
The same John who received and wrote down the Revelation that Jesus Christ showed him also wrote the Gospel According to John. He began that Gospel by explaining that Jesus Christ is the Word (John 1:1–3). As the rider of the horse is Jesus Christ, it is not surprising to read the same name now attached to him.
Further, it is not uncommon to give nicknames born from some characteristic feature of the recipient. The means that Jesus Christ has used in the course of the new dispensation to conquer his enemies has always been the word of God, specifically its preaching (Revelation 14:6–7). That he is now
called
(notice the verb is passive) by his weapon of preference highlights that the (Christian) public attaches the means intimately to the rider.
The name The Word of God,
then, confirms his identity (per John 1) as well as the success of his chosen weapon.
13 He is clothed in a robe dipped in blood, and the name by which he is called is The Word of God.