It's Murraya - "Mock orange". Has sweet scented (some people would say a bit sickly sweet) white flowers in warmer months. Unless it is used as a hedge, which is fine but it often gets no chance to flower.
It depends on where the trunks are, really. You could probably cut it back quite hard with hedge trimmer, but as you say, you'll be looking at sticks for a while. Worst prospect is being too hard and killing it... or sections of it.
Otherwise 10cm isn't very much, you could probably just prune it that much and then keep it to the same level.

With normal hedge trimming, hedges tend to creep out a little bit each year. I tell my customers that each five or ten years, they may need a "sacrifice trim" To get their shrubs back to proper size. Choose the mildest week in spring, when there will be not frost and likely no scortching weather. This would be a good week, except that you guys are upside down over there, so you would probably best wait six months. With most hedge shrubs, you can cut back as everely as you can stand. The vigorous spring growth will come out within four weeks and you can resume normal hedging for another five or ten years.

This advice applys to plants that have the ability to put out new sprouts from old wood. Junipers, arborvitaes, and other conifers may be special cases.