4. Katherine Pulaski
With the low ranking I gave Dr. Crusher, it should come as little surprise that I am a Pulaski apologist. She is a character full of personality who embraces the galaxy’s infinite diversity while also having a healthy dose of skepticism that keeps the crew (and the audience) grounded and reminds us we can’t always accept things at face value.
The frequent critique of Dr. Pulaski is that she is a knockoff of Dr. McCoy, and while the resemblance is certainly there, Pulaski is her own character and a lively part of Star Trek: The Next Generation's second season. There’s also an indication that she is one of the best physicians in Starfleet. Maybe they could have not given her Bones’ disdain for transporters, though.
3. Leonard “Bones” McCoy
Speaking of Dr. McCoy, Star Trek: The Original Series would not have worked without him. Although his acerbic complaining about seemingly everything may seem like a negative trait, it counterintuitively displays the deep care and compassion that Bones has for everyone. He may chide Mr. Spock and Captain Kirk on occasion, but it is because he cares and because he knows that is how they will listen.
The top three doctors are hard to assign hard-and-fast ranks to, because they are each excellent characters who really capture the spirit of practicing medicine in situations where they must adapt on the fly and deal with phenomena and physiologies they’ve never encountered before. As the first main Trek doctor, we have Leonard McCoy to thank for establishing that ideal.