brojek, welcome to WebmasterWorld.
Is there a way to optimize his site and blog for higher SERP for all variants of his name?
One of the problems you encounter when optimizing a site for reputation management is that, for most names, at the default 10-results per search page setting, Google is likely to display only one page per domain at a time in the serps. There are exceptions for infrequently-searched "long tail" phrases, where Google might show two or three or more pages, but I wouldn't count on that happening in this case. So, no matter how many pages you optimize in the doctor's own site, only one of them is likely to rank at a given time... and you will need to fill 9 additional spaces with pages from domains external to your own.
In a normal search for a moderately high-profile professional, you might also encounter the "entity" or business in the Knowledge Panel, on the top right of the search results page, particularly if the name is searched together with a Placename of some sort. Related and suggested searches might also appear... and you might also be wanting to suppress search results with the word "review" appended. Google Knowledge panels and "Business Cards", as they're being called (subject to change), also themselves invite reviews and suggest related searches. Google autocomplete suggestions may also be (or become) an issue. So, the spectrum of complicating factors is wider than you might think.
The ranking factors are pretty much impossible to explain succinctly, as the 'universe' that Google looks at is expanding. I'd do a lot of test searches, actually on other people's names, as there is a remote possibility you might influence Google's view of a search term simply by too-frequent searching over an extended time. You also need to be aware of personalization occurring on whatever browser you or the doctor might be using.
Probably his own site should include onpage the most inclusive set of vocabulary. Inbound links and their relationships are of course another factor. Since you will be creating multiple pages here, you're going to need to be very careful about signs on the web that might flag these pages as being closely related or having common ownership.
It's not an easy problem, and, in a way, it's not a project that can simply be called finished. Depending on the situation, some results over time will disappear but other results may unexpectedly start ranking.