You aren't missing a job title, you're missing a role. You may also be missing the team capacity to fill the necessary roles for what is essentially a second project.
The Business Analyst Role
[W]e need to conduct requirement analysis/impact analysis before getting anything done.
This is typically the role of a business analyst, although it often involves coordinating with the development team and stakeholders. While the Product Owner (PO) in Scrum has a lot of responsibilities similar to those of a business analyst, the PO role is really much bigger than that.
The person (or people) who perform analysis and reporting need a skill set, not a job title. If you have developers who have the skills to perform business analysis, fine. If not, then giving them a temporary title won't make them any more competent in that regard.
In other words, what you really need to do is define what responsibilities this missing role should have, and then find someone within your organization with the skills to manage those responsibilities. It doesn't matter if their job title is Product Owner, Business Analyst, or Senior Bottle-Cap Collector; it's the role that's important.
[O]ur client is asking [us] to work [on the] next major release (parallel development).
Creating a Product Owner or Business Analyst role will not solve your capacity problems. Your team is already fully-committed to working on the current release. Once you fill the missing analyst role, who is going to do the actual work on this parallel release?
The correct thing to do would be to create a separate team to work on the parallel development. Asking your existing team to work on two separate releases at the same time increases overhead, reduces efficiency, and will probably lead to over-engineering or cross-contamination of requirements.
At this point, some folks may object that they don't have the organizational backing or financial resources to run two teams. That's fine if the business accepts the process or schedule risk; just be cognizant that you are taking a sub-optimal approach, and don't expect one team to do the work of two.