The phrase "to be in the public eye" means that a person or thing is being noticed or observed by the general public. They are attracting attention and their actions or behavior are being watched by others. Full definition
You kind of have to not be in the public eye for a period of time while you truly are trying to deal with some of the issues. (inc.com)
However, they haven't been in the public eye to any great extent. (fourwheeler.com)
«Remember you are not a celebrity like a movie star, it's not about being in the public eye because that's what drives your business,» he says. (fastcompany.com)