It's sort of a vague question. I am an ex-system engineer and I am not sure this means what you think it does.
1) There are many different systems in an organization, and a systematic view can be taken of the various perspectives of the organization itself.
2) It is the job of the management of each system to improve it's efficiency
The usage of the term "systems design", "systems engineering", "systems architect" in the instance of the organization I worked for always referred to equipment rather than the way the company worked. Peruse Monster.com with that job title and you will find the same thing.
However, I do think what you are describing is a real job so lets figure out what it's called. Taking a flying guess here, and I am guessing you are either looking at (A) improving the way people work together in a system, (B) the system the organization follows to go from the resources it has to whatever it produces, or you are talking about (C) improving any and every system in the organization.
(A) The first is actually called enterprise architecture. It is the development of how teams are organized within a company to most effectively and efficiently get what needs to be done accomplished.
(B) The second is actually not as penetrable to "change and improvement" as you think since a large portion of what you might call the "manufacture" process of any organization's progress consists of factors that, in themselves, already have much expertise available... such as acquisition of critical resources, manufacturing efficiency, etc.
(C) The third isn't totally possible as a profession, but the closest thing is consulting and often is more along the lines of bringing in someone from outside the company to make lay-offs since that is something people already in the company are ill-equipped to do. As for a job of someone who gets to say how the company will be run as a whole... change whatever they want to make it "better", doesn't exist. Only people who get to do that are CXOs, and they rely on performance metrics to make those changes. Those performance metrics are generated by the management of each "system" or team in an organization (see point #2 above).
If I were you...
- Identify what perspective of system (point #1) you are talking about... is it people, finances, computers, what? There are positions with organization influences for all.
- Decide where on the chain you want to operate. Architects>design>engineers (the nomenclature is different depending on the perspective of the point above... this is for technical systems). Being at the start of the chain might seem enticing, but you rarely get into the nuts and bolts which is where people often notice inefficiencies like what you've said you see needs improving. The engineers are the ones who actually change things that need to be fixed and drive input backwards up the chain for future improvements.
- For technical aspects of organization, programming is helpful but not required (unless, of course, you work in software). Engineers who know how to program will distinguish themselves from their co-workers if you know how to automate certain tasks with a program.
