@BrianCuthbert ...
Out of curiosity, are you using the FFT (Free For Teacher) version of Canvas, or does your school have a paid Canvas environment? A FFT Canvas environment would have a URL of https://canvas.instructure.com/, and a paid Canvas environment would have a URL similar to https://SchoolName.instructure.com where SchoolName is the name of your school/college/university. If you were using the FFT version, there may be several students with the same name, and so as I mentioned before, searching for that person based on name and then by some other unique identifier, might not be as easy as knowing a unique e-mail address, for example. Again, most of the time, enrollments are handled by someone in the school's IT department who is a Canvas administrator...so having to enroll people manually in courses isn't really something that instructors have to be too concerned about. I used to work at a Technical College in WI, and now I work for another College in MI. Both schools have a process to upload students from their SIS (Student Information System) to Canvas which doesn't require going through the course "People" page...as there are other back-end ways to get students enrolled in the proper courses.
If you feel that adding students by name would be beneficial to the "People" area of a course, you could submit this as an Idea here in the Community so that folks could later vote on it and evaluate it. There are a few documents for you to look through under the heading "Ideas and Themes" at: Instructure Community Guide - Instructure Community (canvaslms.com).
To start your Idea, go to: Canvas Ideas and Themes - Instructure Community (canvaslms.com) and click on the blue "View and Submit Ideas" button. Then click on the blue "Submit an Idea" button.
Hope this will help in some way.