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The member names need to be unique in OLAP. So, for example, you cannot have member "Q3" report up into both 2012 and 2013. The standard solution is to concanate the member names in some way. E.g.
There are, of course, many ways to create unique member names and you can certainly do something more elegant than this. But however you do it, the member names must be unique and each unique member name must have only one parent in a hierarchy. The same holds for your geography dimension example.
There is another solution, which is to have separate YEAR, QUARTER, MONTH, and DAY dimensions instead of a single unified TIME dimension. But you should only do this if you have to since adding three more dimensions to your cube is significantly more expensive that adding unique prefixes to member names. The only reason you would have to do this is if you want to break out your report by the separate levels. e.g. give me the sum of Q3, month 8 data over all days and years. This is not common.