What is the name of the sugar molecule in the DNA helix?

Deoxyribose.

DNA is short for deoxyribose nucleic acid. The name tells you a lot about the structure of the molecule.

The backbone (sides) of the DNA molecule are built of alternating sugar (deoxyribose) and phosphate unit. The DNA molecule has two strands of sugar-phosphate units.

In between the sugars are the nitrogen bases. The bases pair up to Chargaff's ratios: A-T G-C

The video below provides a review of DNA structure. That discussion starts at 1:28.

Hope this helps!