My response makes an assumption that your test team is part of the engineering/R&D organization. AND that the issues reported are coming from the end users who are last mile consumers of the product that passed your teams quality gate.
First, you are moving up the value chain to contribute in your organization as a manager now, which means a lot. Just because you are now going to build more talents with all the experience and the nitty grittiy and the tricks of the trade and the ideas that you have had as a tester. You are not just going to wear the the hat of a technical specialist in your trade but also of someone who is now responsible for the aspirations of your team. So, congratulations.
Now for the triage of issue reported by the users, I feel its a great opportunity to be involved in this process as this is the feedback loop that would give you a lot of insights on the processes that you followed internally at test before the product was deployed. Ofcourse it depends on how huge is the flow of issues. If that’s something that doable in your day to day work, go for it. Although i would suggest asking for a resource to do the first level filtering before you take a dip at it. In many organizations, the issues reported from the end users first goes through the different tiers of support and by the time it reaches the engineering teams, its actually proven to be an issue that needs a fix. But that depends on how big the organization and how massive is the flow of issues.
As for the name, QA Manager is just fine, you don’t even need to have the support tag added to the title. If “Assurance” bothers you, try QE, for Manager, Quality Engineering. What i feel you need to focus on is, Is there any learning to do with the feedback from users, will these feedback’s help strengthen the quality processes internally, will these feedback’s help the test teams to provide/preempt design flaws in the first place.
Personally, I feel what you hear from end users could be very valuable to your growth as you move ahead.
Hope i made sense.