Can I put neosporin on my dog?

I'd advise you to call your vet. It may not need an actual appointment, but depending on the location and depth of the cut, they may recommend a dog-formulated quick drying healing spray. One concern is that any ointment formulated for humans that you'd apply may be ingested by the dog licking it off, which could be worse than not applying anything and simply keeping it clean and dry,

Yes you can use Neosporin two to three times daily. Be sure to keep the area clean and try to prevent your dog from licking it.