What is the best order of columns on a compound index?
In MySQL, the order of the columns in an index is very important. Searching over an INT is faster than search on a string(VARCHAR). So an index on (organisation_id, name) would be better than that on (name, organisation_id).

If a WHERE clause satisfies the prefix an INDEX then that INDEX is used. So no need for a separate index on organisation_id. The existing index will take care of it.