That absolutely sucks, and does put the rejections in a bad light, but names don’t directly affect your behavior. Religion is different in that regard.

> What about your name? Do you have to give that up too to culturally integrate?

In the past you had that too yes, your name was transformed into a French equivalent.

I guess you could say freedom of religion is a human right but it's not a human right to be culturally integrated. And so you could absolutely be required to give up that freedom in order to integrate, in the same way your workplace may require you to be at your office and do certain things, which is clearly not a violation of your freedom.

> - So In a majority christian state, is it ok to discriminate against jews?

People would still be discriminated for wearing a big cross in France as well, it's just not that common.