이름 corresponds to "name" closely. What we call people and pets by is their 이름. We also use 이름 for things, such as countries, places, roads, buildings, events, and so on. Just as in English, however, there is also 제목 (title), that we use for the name of works such as books, movies, and others. 이름 can also work for these sometimes (especially books), but 제목 is generally more proper. In short, you can generally equate 이름 with "name", and 제목 with "title". One exception is that we never call peoples' title (i.e. their position in an organization) 제목. The word for that "title" is 직함 (직책 and 직무 are also used sometimes). 제목 is strictly "subject title".

As far as I know, yes. And with movies, restaurants, etc. In fact, the problem is Koreans speak English that way too; they always say 'what was the restaurant's name? or 'what is your sister's name?' instead of the more natural 'what was the restaurant called?' or 'what's your sister called?' :)