Why is the list being built?
In my experience, these lists consist of a lot of entries that will be used for some kind of bulk action. You want to make the building process as light on clicks and maintenance as possible.
One time interaction
In response to the update ... If users will only be interacting with this control one time to get their account set up, there is little time for learnability. The pattern chosen must be familiar or highly self-evident. With around 10 entries, clicking each one is no big irritation compared to the barrier of learning a novel or more powerful pattern. Place the action button adjacent to or within the name column so the user can quickly scan and click to add to their list. Adding that selection to the list below in real time will make the whole process reassuring for the user.
Don't forget to allow removal from the list!
One by one
Your example implies a short list, where building new lists won't happen too often. If those restrictions are true, then interaction with each add is okay and an "add to my list" button is doable. Drag and drop is also a good option for desktop use. I might also allow for selection of entries (like a checkbox) that activates a bulk "add" button.
One challenge with the one-by-one approach is that the user should be able to click at the point where they determine inclusion. In other words, if the name/job title field is likely to be the point under consideration, you'll want to allow the user to interact at that point. In your wireframe, the user has to first locate the desired row by the relevant column, then scan right to find the button. That's tedious and error prone.
If you are going to support large list building, you'll need a more automated flow. Something like a "smart list" that watches for a defined set of parameters (positive and negative) to automatically add to the list.