Hi Sabine,
Yes, I have a registered business and as a full-time freelancer I'm allowed to deduct all business related costs. I keep track of all costs (invoices, receipts) and my bookkeeper handles the tax return and everything.
Are you doing this work on the side? Are you employed? Then the Belastingdienst will likely classify your revenue from Fiverr as 'resultaat uit overige werkzaamheden'. But even then you should be able to deduct most business-related costs (phone, computer, software subscriptions, Paypal fees, etc).
Maybe there is a treshold for that if you're not classified as a full-time 'ondernemer', so always check with an accountant. I'm not a tax expert so don't take my advice for granted 🙂