If it's OK to change settings before reload, you can use a variable vLanguage with possible values 'English'. 'Dutch', etc., and check its value in the script. Depending on value, use differrent SET MonthName statements. Certainly all users of the document will see the same language wich was selected before reload. If this is not acceptable, there solution will be more complex. For example, you have to keep multiple month fields and show them depending on language.
In this case you have to keep Months in all languages you use, for example Month_E and Month_D. How to show them is up to you. There could be conditional show of objects with different Month fields depending on vLanguage variable, or calculated dimension in each object, like if(vLanguage='English', Month_E, Month_D).
I tried to use this solution for months and it's working fine on charts, but when I try to create list box I get all of the values in every language available on the filter. When I choose one of the languages I get its monthnames at top and the other language's months appears as well (with gray background as they're not selected). How to get rid of them and show only the values for selected language?