Here are some popular haircut names:

1. Fade
2. Undercut
3. Pompadour
4. Quiff
5. Pixie Cut
6. Bob
7. Layers
8. Shag
9. Crew Cut
10. Mohawk
11. Side Part
12. Taper
13. Comb Over
14. Ivy League
15. High and Tight

Let me know if you want more!