If your dog is regularly vaccinated against rabies, there is no need to worry about rabies.
If the bite is to someone in your own family, honestly, there is no need to be nervous; dog owners getting scratched by their own dogs is common, so be sure to vaccinate against rabies regularly, and use imported vaccines.
If the bite is to a stranger, then there might be no way around it—you will have to pay for their vaccination. No matter what you say, people will not feel at ease.
When I first raised a dog, just like you when the puppy first came home, I was scratched on the neck by my dog. The dog's nails were a bit long at the time, and I was very anxious as well, asking other dog owners everywhere. People said it was nothing, as long as you wash the wound well and apply iodine. Later on, it really turned out fine.
If only a bit of blood came out, wash the wound with tap water and soap thoroughly, try to wash until the wound appears pale, then apply iodine. Do not bandage the wound; it should be exposed to the air.
Rest assured, as long as your dog is fine within 10 days, you will definitely be fine.
Of course, if you really feel uneasy, you can also get vaccinated, hehe.
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You can disinfect immediately with alcohol, and if you’re really worried, then go to the hospital to get an injection.