In many places, a title column is asked where I fill Mr. After getting my PhD can I "officially" change it to Dr.? Is this country dependent? I want to know about India, DrUK and US.
PhD is an academic degree. It is actually dependent on person and country whether to use the title "Dr." in passports and other relevant documents.
However, using Mr. would be wise to avoid a confusion between a doctor (MBBS, MD) and a doctorate (PhD). As per UK gov website, it is not advisable 
I have never come across anyone using Dr. in legal documents. Moreover, it is not really a necessity to include Dr. in official/legal documents. For example, I still see my supervisor (who is a senior professor with PhD in 1990s) gets official documents with his name titled "Mr.".
As far as the USA, their passports do not have a title field for marital status (Miss, Mrs) professional titles (Dr, Rev, etc) or for titles or nobility (Dame, Sir, etc) so it’s a moot point for American passport holders.
I think it depends on you whether you use Dr. or not. Getting a PhD is a very important and difficult accomplishment and you should feel proud of it. If you want to use Dr in any circumstance including in your passport (if allowed) go for it. If you don't feel like it then don't. I don't get why people would be worried about being confused with a MD A MD is a Dr just like anybody else, it has no higher or lesser importance. If someone gets confused then they can ask you what you are a Doctor of. My suggestion is use it whenever you feel like it, you worked really hard for it.