No, they probably shouldn't be calling your neighbor. Are they in violation of any law, not sure? Generally, collection laws only apply to 3rd party collectors. Your mortgage company is a 1st party (meaning, you are directly liable to the mortgage company), so most collection regulations don't apply.
More information would be needed to know whether it is legal for them to do that. Are they discussing your financial situation with the neighbor? Did you list the neighbor as a reference when you took out the loan?
It depends on the reason for their call but there are very limited times in which they can contact third parties about your property or the now-discharged debt. They may have violated the FDCPA or committed a sanctionable action.
Advice on this forum is for informational purposes only and should never be mistaken as a substitute for legal advice. If you are in need of legal advice, you should consult local legal counsel.