Upvote:5
If you answer yes to that question you will be asked to provide details of your previous name, and almost certainly nothing more.
All countries track visitors to their country, even across trips, so that they know how many times you've visited, how long you've been in the country, if you have been warned/banned by immigration/customs/police in the past for any reason, etc.
If you change names - which is a common practice for many people around the world (the most obvious being women in many countries when they get married) - then immigration may no longer be able to track your previous stays as they may see you as a different person. Answering this question and providing your previous name will allow them to join the records for these two 'different' people into one.
Note that answering this question incorrectly doesn't mean that they won't be able to detect your previous details/visits. Many of the details on your passport will have not changed (eg, date/place of birth, and likely at least some of your name), which when used in conjunction with the bio-metrics that many countries capture when you enter (photo, fingerprints, etc) they still maybe be able to determine your previous name - at which point you would likely experience difficulty due to answering this question incorrectly, which would likely be seen as an attempt to circumvent the immigration procedures in some way.
So in summary, answer it correctly and you'll get an extra question or two. Answer is incorrectly and you could be in for a lot more questions and trouble - which is true of most questions on an immigration form!