Disable "helpful" iMac message icon when text with my iPhone

So, now that I have my new iMac 5K, I'm pleased that it can text like my iPhone. My Windows PC of course cannot. BUT I do NOT want anyone sitting at my iMac to read my text messages, or even know to whom I am texting.

My question is, can I disable the nonhelpful message status icon that iMac throws up when I text on my iPhone, but still use the iMac as a text machine whenever I please?

Thanks, Ed

Yes, this can be done.

The best way to restrict access to your Messages is to use separate login accounts for each person using your iMac. Each account would then only have access to their own Messages.

If you would rather not set up accounts for everyone, you could simply turn off the alerts on your screen within the Notifications Preference Pane in System Preferences by turning the alert style to "None". However, this would not stop someone from simply opening up the Messages application to see all of your texts.