Scam letters may use “official” sounding names like “Domain Authority” with the American flag to create the impression of a trusty national organization and scare-tactics and deceptive language to make people think that their domain may be about to expire. Upon careful reading you’ll find they’re actually offering a “business listing” in some unnamed or unknown directory, usually at a much higher price than “real” domain registration fees cost.
Listings on the the most important maps and directories such as Google, Apple, and Bing are free. Some dental-specific directories may charge a fee, but this would have nothing to do with your website domain “expiring”. Paid dental listings usually provide additional benefits besides just the listing itself, for example appointment booking, provider directory for a specific procedure, etc.
When in doubt, always ask your website company directly. Never pay without checking first in response to scam letters!