It's important to understand that in MDX you are building sets of members on each axis, and not specifying column names like a tabular rowset. You are describing a 2-dimensional grid of results, not a linear rowset. If you imagine each dimension as a table, the member set is the set of unique values from a single column in that table.
When you choose a Measure as the member (as in your first example), it looks as if you're selecting from a table, so it's easy to misunderstand. When you choose a Dimension, you get many members, and a cross-join between the rows and columns (which is sparse in this case because the names and genders are 1-to-1).
So, you could crossjoin these two dimensions on a single axis, and then filter out the null cells:
SELECT
event_count ON 0,
TOPCOUNT(
NonEmptyCrossJoin(name.children, gender.children),
10,
event_count) ON 1
FROM
events
Which should give you results that have a single column (event_count) and 10 rows, where each row is composed of the tuple (name, gender).
I hope that sets you on the right path, and please feel free to ask you want me to clarify.
For general introductory material, I think the book "MDX Solutions" is a good place to start: http://www.amazon.ca/MDX-Solutions-Microsoft-Analysis-Services/dp/0471748080/