I'm growing a curly willow, started from 4 bare stalks from a friend at a florist. Is there another name?

Having trouble finding info on this tree? bush? and was wondering if there is another name for it? It has grown huge in just 3 years, want to plant more but afraid of the stigma willows have for being invasive -- roots uprooting houses, etc. And what about my near-by septic bed?