Good question. I don't know for Java, but with ICU4J you should be able to use LONG_NAME: http://icu-project.org/apiref/icu4j/com/ibm/icu/util/Currency.html
I assume that is the name you are looking for - something like 'US dollar'?
Methods to retrieve currency display names will be in JDK7.
The feature is already implemented in the current build, so you can try it out.