This is true.
This feels wrong. If you’re going to ask for my name only for asking sake then it shouldn’t be there in the first place. I suggest that if it’ll remain, you could use it to address the user in future replies (it’ll create some sort of bonding).
Finally, if there is a way you could tell that the user doesn’t want to supply a name, you can add a fun twist to it and call the person J. Doe (J could be Jack or Jane that’s why I left it as “J.”)