EU GDPR and Data Processing

We provide a service to our customers whereby we provide a technical support service for certain software applications that they run. If a customer employee experiences a problem with the software application, they will log a ticket with us and we will diagnose and fix the problem. In certain circumstances, we may transfer the ticket to our partner in XXX to help diagnose and fix the problem. The ticket has details of the technical problem but includes the customer employees’ name and e-mail address. We (or our XXX partner) may use the e-mail address to reply to the employee and keep them informed on progress or request follow-up information. Would this data be classed as “personal data” and if so would we be classed as processing this personal data? If yes to both, what steps would we be required to take to meet our obligations under the GDPR regulations?