I'm afraid Ouchy is going to be called ouchie outside Australia as well. (Need a bandaid?)
Several articles state that the tower/castle there was built by l'Évêché de Lausanne in 1170, but none seem to say why it's called Ouchy. I wonder if Ouchy could be a "corruption" of Évêché.
According to fr.wikipedia.org via babelfish.altavista.com,
Évêché is the episcopal see of a bishop.
However, two directions apply in this term:
Episcopal city where a bishop lives and where finds the cathedral of a diocese;
Usual residence of a bishop, located in this same city.
Caution: évêché and diocese are not synonymous (against example are the 9 évêchés of Brittany).
If my wild guess is true, your friend named her child Bishopric. I think I'd rather be called ouchie.