Which role is the equivalent to the Product Owner in DSDM's Agile Project Management? Would the Business Ambassador play a similar role?
The Business Visionary role comes closest. However, there is no 1:1 mapping between DSDM roles and a typical Product Owner role, especially as defined by the Scrum Guide.
The DSDM Agile Project Framework contains a Roles and Responsibilities Handbook. In contrast to popular agile frameworks such as Scrum that assign product ownership to a single individual, DSDM spreads a number of product owner responsibilities out among several different roles at both the Project and Solution Development levels. There is no single person who encompasses the Product Owner (PO) role as defined in Scrum, but the Business Visionary role probably comes closest.
The DSDM Roles and Responsibilities Handbook defines the Business Visionary role in Section 7.4. This section says (in part):
This is a senior project-level business role that should be held by a single individual, since a project needs a single clear vision to avoid confusion and misdirection. More actively involved than the Business Sponsor, the Business Visionary is responsible for interpreting the needs of the Business Sponsor, communicating these to the team and, where appropriate, ensuring they are properly represented in the Business Case. The Business Visionary remains involved throughout the project, providing the team with strategic direction and ensuring that the solution delivered will enable the benefits described in the Business Case to be achieved. At the end of the project, the Business Visionary will own the Deployed Solution and will be responsible for the realisation of any benefits associated with it.
Among all the roles within DSDM, this is probably the closest to what most agilists would consider a typical Product Owner role. However, the full functionality of a Scrum Product Owner is really spread throughout the project-level business roles of Business Sponsor, Business Visionary, Technical Coordinator, Project Manager, and Business Analyst (see § 188.8.131.52).
Consolidating "Product Owner" Responsibilities within DSDM
It is also worth noting that § 7.16 of the Handbook explicitly says:
On a DSDM project, one role may be fulfilled by several people, or one person may fulfil (sic) several roles.
Whether one person could really encompass the totality of a typical Product Owner role within the DSDM framework is questionable, but the framework technically allows for it. Your mileage will therefore vary.
Caveats and Assumptions
The original question didn't really define its terms. Because roles can and do vary by framework, I chose to compare the DSDM roles to the Product Owner role in Scrum. Other agile frameworks may or may not use the term "Product Owner," but it's useful to have a baseline for analysis.