I think you will find that the word “name” doesn’t mean appellation, rather “authority”. To say that the word “Jesus” has some power in itself is superstition or magic. It is by Jesus’ authority that we act, not on our own (in our own name).
When a servant or disciple says something on behalf of their master are they doing so in their own authority or on the authority of the master?
If Jesus, who is the master, tells his servants to baptize in his name, he means with his authority. Precisely what is commanded in Matthew 28:19.
Ergo, the words matter because its about who is operating under whose authority and on behalf of whom.