Yes, you need to request a tax number from NAV (Hungarian Tax Authority), which enables you to issue invoices to guests. You can apply in person at any NAV office or online (sole proprietors must apply electronically).
The form number is: XXt101 (where XX is the current year, e.g. 26t101), NACE code: 552014 "Private accommodation service".
Tip: if you don't have your permit yet, you can initially register for "long-term rental" and modify it to short-term after receiving your permit.
