Basically yes. Of course the correct name for the country is United Kingdom of Great Britain and Northern Ireland. But that's rather a mouthful, so we want something shorter. "Britain" is as good as anything and it gets used all the time, including by British politicians. Especially as the adjective is "British" and my official status, which it says in my passport, is "British Citizen".
You have too many picky answers here who are confusing Great Britain with the way "Britain" is used as just another way of saying "the UK". Look (and I'm saying this more to them than to you), we all talk about Britain and when we say that we all know we mean the UK.
I see from your previous questions that you're fairly obviously in the USA (sorry if I got that wrong) and that's a country that has the same problem. Maybe you'd say you're American. Which people will criticise because America, really, is a whole continent. But of course "United Statesian" is just daft. We just have the same problem. "I say potato, you say potahto, I say tomayto, you say tomahto, let's call the whole thing off!"