I searched thru the Apple Support pages but could not find a way to set this up. But they did suggest you contact Verizon and see if they can help. Hopefully they can. Yours is a reasonable request.
This USA Today article offers some suggestions.
https://www.usatoday.com/story/tech/columnist/2020/06/04/kim-komando-has-5-tips-block-hide-your-number-when-making-calls/3138344001/
But FYI, I tested calling by using *67 immediately before the number. It not only blocked my phone number, but it blocked my name, as well. The article's suggestion of using a burner phone may be your best bet if Verizon cannot help.
One last suggestion - If you want to keep it as simple as possible, call using your iPhone and if a patient does try to call you back on that number, you can always block them.