No - the nickname is only visible to you. If you want to change your course name and have it visible to all, it must be done through the settings tab of your course.
Students will not see your course nickname.
However, anyone with permissions to "masquerade" as you, such as Canvas Support or your school's Canvas Admin, will see your nickname if they are logged in "as you" using the masquerade function to troubleshoot something. (I'm not sure if they have any way of seeing it otherwise, but they won't see it by default if they are looking at the course "as themselves".)
Similarly, I, as a teacher. can't see what nicknames students have given my course unless I'm looking over their shoulder as they're navigating their dashboard while logged in.
Both @abunag and @thompsli have given you great answers here. I'll just add that you can also find more about this by visiting this Guide: https://community.canvaslms.com/docs/DOC-10163-4152719653 (Check out the section called "Create Nickname".) Since you've received some correct responses here, I'm going to mark your question as "Assumed Answered" rather than marking one individual response as "Correct". I hope that's okay with you. Thanks for posting your question here in the Canvas Community!