I have list with doctors sorted by country. When a user chooses "Germany" they will see doctors from Germany. When that happens, I change URL e.g. 'example.com/list?=germany' but I do not change <title> of the page. The title for "Germany" is same as the whole list or as it is for doctors from Italy.
Is this fine or do I need have special <title> for each choice? Will Google think that using the same title indicates thin content or spam?
You should have a different title each time you change the URL. That includes changing a query string parameter.
Google won't think that your site is thin or spam with many same titles, but it may think many of your pages are too similar to index. Changing the titles will help you rank for "German doctors". Without changing the page titles you would be very unlikely to rank for that.
When you add your site to Google Search Console, Google will tell you tons of information about your website. One of the things that it will list is pages on your site that have the same page title or meta description. Google suggests that you write unique titles and meta descriptions for each and every page (different URL) on your site.
I usually recommend writing a meta description for good SEO. It is used to control the snippet in the search results. Writing a good meta description can increase the click through rate compared to whatever snippet Google chooses. A good meta description uses the keywords ("German doctors"), includes a call to action "choose a doctor", and may have additional details that make it more compelling. eg: "Choose from among 340 German doctors rated by customer feedback, qualifications, and medical success rate."
You also indicate that you have some other types of parameters that should be handled differently. Sorting parameters do not change the page contents. For those you usually want to tell Google that those URL variations are for the same content. You usually do so with a link rel canonical meta tag. You tell Google the preferred URL for "German doctors" and have all other sorting of them point to the preferred version. Users usually like a version where the "best" items are at the top of the list. A good canonical would be one where the top doctor is available and well rated.
Say you're looking for german doctors, or itialian doctors, would you:
Search engines try to work like humans do. Optimize properly for humans and bots will often reward you for that.
Apart from that, not doing the different titles will result in "Duplicate titles for the following urls", so you want unique titles, descriptions, etc. The combination of the title and description will be shown in Google, that combo should trigger people to visit your page, so a unique description would give the user a better estimate of what they're going to get.
For other additions to the url, like sorting, add a canonical tag to your pages. This way you tell Search Engines "we're are sorting, but it actually still the italian doctors page, so no need to index this page specifically".
