It has happened several times that I needed to spend quite some time and effort to explain my role as a manager that manages a team around 10 people. My team builds a webapp for outside customers. My role combines a role of product manager with a role of software architect (and manage the people). I have final say for both product and technical decisions:
The product role is similar to the product owner in scrum: I get requirement from my customers; I manage the product backlog, decide the priorities, In a word I decide the product roadmap.
The architect role is to make the most important technical decisions. For example, I decide which tech stack for frond-end & back-end.
Scrum uses the term product owner so people who are familiar with scrum sometimes will response with "But scrum doesn't suggest PO touch the technical side". Other times people will response with "So you are a technical/development manager. But should you work on product side?"
"The Manager's Path" use the term "engineering manager". But I feel "engineering manager" can't convey my role too. In way I think product owner is a good name because I indeed own the product, every bit of it. And to delegate and work with the team is the key to do both roles right.
So is there an easy way to explain my role? Is there a a well established name?
Right now I sometime say I am the Product Owner as scrum defines plus technical manager. AND I will further emphasize that I have enough scrum experience to say what I mean here.
--- update ---
I came across this answer on quora, described the similar role at amazon too (the answer was in 2011), not sure it is still relevant.
On some teams, there are no Product Managers, and the Dev Manager owns both the product/business and the technology. We call these people "Single Threaded Leaders", though their formal role description might be Dev Manager.
This article used the title "Technical Product Manager" and mentioned the advantage I said,
Their experience helps them avoid the pitfalls of requesting things that are infeasible or too large of an ask for the allotted development cycle.