Tell customers before they guess
Publish a short note that says what is changing, what is not and who to contact. Silence is read as bad news.
Keep the contact points stable
Do not change the support address, chat or login without notice. Forward old addresses for as long as customers use them.
Prepare answers to the likely questions
Draft replies for pricing, contracts, data handling and roadmap, and have the right people approve them.
Merge tools in stages
Move the queues one at a time and keep the old inbox forwarding. A big-bang switch risks lost tickets.
Watch for early signs of churn
Tag tickets that mention the change and review them weekly. A rise in cancellations needs a quick response.
Keep the team informed
Support hears about it from customers. Give agents the facts first, so they are not learning from the same messages.