How would you lose your identity? Unless you base your entire identity on your nationality.
It's big part of our identity. As being born in European country I share most of the values of Christianity. That is despite being an atheist. If we try to diminish that values we expose ourselves to indoctrination of values of others maybe not as liberal as our cultures. We shouldn't, in my opinion, dilute our identity we should cherish and embrace it.
I give you an example. In Europe, at the moment, there is a trend to invite and harbour people from Middle East. As much as noble it is, a big part of these people have no intention to integrate and at least respect our values. It is quite opposite, the core of their values is to indoctrinate others to their liking.
Identity preexists nationalism. No one says that identities did not exist prior to nationalism as an ideology. You can have an identity, without being a nationalist. You cannot be a nationalist, without having an identity. Nationalism is an ideology. It is not tautonymous with the concept of identity.
Identity is primordial, nationalism is a modern construct. They are not exactly apples and oranges, but more like using oranges to make marmalade.
I shall point out to you that probably every kind of social change and transformation was, due, at least in part, to a disagreement, or the emergence of something new and different that broke pre-existing patterns. Whether we speak of the emergence of the concept of citizen, through the collective struggles of all common peasants against the cultural hegemony of aristocracy; or the abolition of slavery and the emancipation of women, through the struggle to expand a previously limited definition of mankind and citizen respectively, sometimes dilution of ideology is not a bad thing at all.
I respect your concern about the impacts of multiculturalism on Identity, and I am not at all suggesting that the above process I explained is always beneficial and / or benign.