Can I reuse an insulin syringe for a second dose later in the day?

Don't. It's false economy. Insulin needles are like 15 cents each in bulk. You want a sterile needle and a sharp tip. A reused needle is duller (more painful) and contamination risk is nonzero, especially if you're pulling from a multi-dose vial repeatedly.

Used needles on second stick hurt like hell. That alone is reason enough.

Also a sterile needle each time means if you get a bad injection site, you know it wasn't the needle.

Ok fair, pitching them.

saving on syringes but spending $80 on peptides is backwards economy.

Box of 100 BD insulin syringes is like $15. There's no good reason to reuse.