When groups are used, the instructor needs to be able to make certain no student has been left out, and students need to be able to see which group they are assigned to.
One way for an instructor to see what groups their students are in is to go to Settings > Users > Enrolled Users. There, the instructor will see their names, the last time they accessed Moodle (NOT the last time they accessed this course!), their groups and more.
To be certain that students can find out the name of their group(s), you can add the People block.
Students should select Participants from the People block and they will see a list of all students in the class. Select User details from the User list pull down menu:
Next, they should click on their own Full Profile, as below.
And, they will see which group(s) they are members of.