it has been a while since i have fired up AdventureWorks, but
select
[Customer].[Customer].Children on 0
from [Adventure Works]
will return the customer name for all customers in this rather flat hierachy, exluding the "ALL" customer. It appears in the 2008R2 release, Last Name is not part of the Customer dimension.
Additionally, the query above will return for each customer, the default measure for this cube, which is Reseller Sales Amount. Because Reseller Sales Amount has no relation to the Customer dimension, and we have specified no other dimensional constraints, we get the Reseller Sales Amount value constrained by the default member of all dimensions related to that measure (measure group, actually).
If we were to select a measure related to Customers, such as below, we would see the Internet Sales for each Customer.
select [Measures].[Internet Sales Amount] on 0,
[Customer].[Customer].Children on 1
from [Adventure Works]
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