I am stuck on the the part where you have to name the constellations. Do I enter the letters on the globe that are shown on the labels of the constellations.

You enter the name of the constellations using the clues given by Iris in her note.

Enter the letters by pressing the correct Greek letters seen at the ring at the middle of the globe.
Click-hold to turn the letter ring.
Place the cursor over the letter and the name of the letter can be seen at top right of the screen.
The letters do not repeat, so once it is pressed down, continue to look for the next letter to be entered.
Thomas will say when the name is finished.