Most people search their own name occasionally. That gives you a snapshot, but you may miss what appears the following week. That is why I wrote about Google Alerts: you choose terms to monitor. A business owner might use a company name, product, competitor or topic worth writing about.
Make the query specific
A broad word quickly creates more messages than you can read. Start with an exact business name or a combination of topic and place. Watch for namesakes and words with more than one meaning. After a few days, see which results actually matter and refine the query. An alert is useful only when you can respond to or learn from a result.
You might notice an incorrect listing, discover a question customers are asking or follow new writing in your field. For me, this is a way to spot opportunities without searching all day.
Know its limits
Google Alerts helps you monitor selected search results; it is not a complete record of everything published about you. You do not need an immediate email for every hit. Choose a frequency that lets you process the results. For important topics, also check reliable sources directly. An alert cannot make that judgment for you.