If you process data relating to people in one particular member state, you need to appoint a representative in that country who can communicate on your behalf with data protection authorities. The GDPR and its official supporting documents do not give guidance for situations where processing affects EU individuals across multiple member states. Until this requirement is interpreted, it may be prudent to designate a representative in a member state that uses your language. Some organizations, like public bodies, are not required to appoint a representative in the EU.