Yes, someone can tell if you are on Facebook if they are connected with you on the platform and you are currently online. When you are logged in to Facebook and actively using the platform, your name will appear in the chat list and a green dot will appear next to your profile picture, indicating that you are currently active.
If you do not want other people to see when you are online, you can change your chat status to "offline" or limit who can see your online status in your privacy settings. Keep in mind, however, that if you take these steps, you may not be able to see when other people are online either.
Additionally, if you post, comment, or react to a post, other people who are able to view that content may be able to see your activity on the platform. If you want to keep your activity private, you can adjust your privacy settings to control who can see your posts and activity on Facebook.