Normally you should not translate the organisation's name (the first time you can mention the translation in italic, between brackets or in a footnote) unless the organisation has -or wants- an international reputation and wants it's name translated.
"vzw" indeed stands for "non profit organisation"and in Belgium it is legally part of the organisation's name. It has to be mentioned with the organisation's name in all references and on all stationary to avoid prosecution.
Your translated text should read "Naam Welzijnswerk vzw" as it should in the original (Flemish) text.