Actually, I'm not sure if you can use the variable directly in the tool.
I think that variables are interprated in System Prompt at the moment of start. So you should use it in the System Prompt and tell the agent to use it with the tool.
Like: "... when you get user name, use the tool sendContactData with the complete name (as name) and the phone number {{customer.number}} (as phone_number).."
Hope it helps!