Terminal has no option to "open new tab" and no label in tabs

This seems to be a newer version of GNOME Terminal update (>3.10). When you open the preferences dialog, you should see something like this:

When you set the "open new terminals" setting to "Tab", the new terminal action will now open a new tab in the same window instead of opening a new window.

The old behaviour regarding tabs seems to have been changed in 3.12 and 3.14, for some reason.

You seem to have updated your GNOME components with a version that does not ship with Utopic, so you should expect to see it break.

Encounter the same issue after upgrade from 14.04 to 16.04. It took me sometime to find the "preference" window as the solution mentioned above in Ubuntu 16.04. In case some other people have the same issue, I share the way to find the preference window. You can find the preferences by: open a terminal, at the terminal right top are the hidden tabs -> terminal ->Preferences