Historic district review limits the sign, so the website has to be the sign
In protected parts of the city the exterior you are permitted to change is limited, which quietly moves your signage budget onto the web.
Practices in the French Quarter, the Garden District and other protected blocks generally work under historic district review for anything visible from the street. Requirements vary and change, and are worth confirming with the city or the relevant commission before you plan anything.
Whatever the outcome, plan for the site carrying more of the identifying work than it would in a suburban plaza. A patient who cannot spot you from the street decides you are closed and drives on.
Show the facade in daylight, from the direction people approach. Show the door itself. Show what the sign actually looks like, at the size it actually is.
Repeat the same photographs in the Google Business Profile and in appointment confirmations. Recognition is what gets somebody out of the car.