I’ve only previously encountered triangulation with goods, not services.
For B2B, there’s probably no change. You wouldn’t charge UK VAT, and your customer would be liable to account for VAT using the reverse charge.
For B2C, you’ve got a choice between registering for VAT in each of your customer’s member states, or registering with a “non-union MOSS” scheme in a single member state. Although if you’re selling via a digital platform/marketplace, the responsibility to account for VAT on B2C transactions may lie with them.