A first-time European customer is asking me for an "organization number" to enter me into their accounting system. Is this a standard term? Is this my (USA) Federal Tax/Employer Identification Number? Or, am I free to make up any number? Or, is there no enough info to understand what's going on here?
It is a number used in Europe that isn't applicable in the US. Just tell them that you are a US company and don't have one. It happened to me once and they were fine with that.
Making up numbers is rarely a good idea.