You are right. "연" is just his or her last name and "실장" is literally a head of the office or the person representing the office. (실 is a Chinese character, which means "room, house, space" 장 is also a Chinese character, which means "top person or head" as you may know.)
I think there is no clear-cut answer on what occasions we need to call a person "실장님". It just depends on what size of the company, what industry the company is in and how they like to name or position employees.
So there are some small companies where the owner wants to be called "실장". It makes sense because he is the head of the office. In other companies, "실장" can be a senior manager or manager, generally.