The reason that immigrants leave their own countries and move to another are many and varied; two of them might be that they are seeking a better life, or that life for them has become dangerous in their country of birth.
When they are choosing which country to move to, their considerations are also varied, but you have to assume that they believe the country they have moved to is one which can provide them with a better future.
Surely they realise that this new country has its own history and culture, that has evolved over centuries to what it is today. Some elements of that history are good, some are shameful, and some are today evident in that culture only in a name. That name might be imbued with the best character associated with that name, and any not-so-comfortable connotations may have faded over time.
A name like, say, Crusaders.
The Crusaders are a Canterbury rugby team, a very successful one with a proud history. The word 'crusade' refers to the religious wars carried out by Christians again Muslims.