Thanks for the responses. I haven't gotten any requests from buyers but it's actually part of Etsy's recommendations:
https://www.etsy.com/help/article/171"Seller Information: If you are a seller in the European Union or if you are selling to, or specifically targeting, customers in the European Union you may need to include the following information in the Seller Information section. This may not be a requirement for sellers in the United States and other non-European Union countries:
▪ Your name
▪ The physical address from which you run your shop
▪ An email address that buyers can use to contact you
▪ Where applicable, your tax identification number"
Etsy leaves it open as to whether you need it but I wanted some confirmation. Based on what you are both saying, I won't include that information until I hear from Etsy about it.