Can Singularity target the same unit twice?

No, you cannot target the same unit twice with Singularity.

According to the official rulings for Singularity:

• Singularity must target two different units if you choose to target two units. You cannot target the same unit twice to deal 12 damage.
• "Up to two units" means you can choose to target 0, 1, or 2 units.
• If you target only one unit, it takes 6 damage. If you target two units, each takes 6 damage.

This is a single trigger that requires choosing distinct units if you want to target two of them.