You're rather missing the point. As I mentioned in a previous comment, they are choosing the name purely due to the connection to the saints, it's nothing to do with wanting a connection to Italy, although of course they like Italy . I lived and worked in Italy for several years, how offensive that you think people wouldn't be able to get their head around the name Cici and would think people were saying 'yes yes'. Italians do know about other languages and cultures? So rude.
The parents also aren't wanting to use an Italian pronunciation of Cici? How odd that this is presumed. I know multiple Siennas who are nicknamed Cici. Should they pronounce it Chee Chee too, because Sienna is also in Italy?
As I also said upthread, the 'see' sound in Assisi is pronounce like this - 'see'. Hence why the nickname is pronounced 'see-see'. It's the same as the name.
Like I also said earlier, I don't know how they are spelling 'Cici/see-see'. I spelled it like this: 'Cici' in this thread, because that's the commonly used spelling of the nickname in English. They might be spelling it differently, I don't know.
But it makes no logical sense for 'Assisi' to have the nickname 'chee chee' when this isn't even in the name?
I can't see any potential 'mockery potential' in the name Assisi, except that there is an 'ass' sound but I know a couple of Astrids who have never had any issue with this. Bullies will bully, they don't need a reason. So sad that you think parents should sacrifice a name that is meaningful for them to appease potenial bullies - in my high school a girl with the surname 'Warne' was ruthlessly bullied because the name rhymes with 'prawn'. Sounds ridiculous now, but it made her life a misery. So bullies will be bullies - they don't need a reason, they'll find one.
I think Assisi is a gorgeous name and I'm jealous I didn't think of it for my daughter!