When you work with attributes in SSAS, there are two properties that affect the members of that attribute. The first property - which is set by default when you create the attribute - is KeyColumn. The column that you use here determines how many members are in the attribute because processing generates a SELECT DISTINCT statement based on this column. It's a good idea if you use an integer value here for better performance.
It sounds like perhaps you have a month number for your attribute here, which is good. Except that you want to display a month name. In that case, you set the NameColumn property with the column in your data source view that contains the month name. This produces the label that you see when you browse the dimension.
That said, it's usually not a good idea to have just a month number or month name because you probably want to create a hierarchy to roll up months by year and you won't be able to do that with just a month name. I wrote a blog post describing how to set up a date dimension that might help you: http://blog.datainspirations.com/2011/05/11/sqlu-ssas-week-dimension-design-101-2/