Is dealing with non-Islamic names – such as names associated with other religions – considered polytheism (shirk) or disbelief (kufr) when interacting with non-Muslims in non-Islamic countries?

Informing about non-Shariah-compliant names, whether in writing or verbally, is permissible and entails no sin. This is because informing is broader than creating [or coining]. Thus, writing names by which people have become known is permissible, even if they would not be permissible when initially coined. For example, our Prophet Muhammad, peace and blessings be upon him, said on the day of Hunayn: "I am the Prophet, no lie; I am the son of Abdul-Muttalib."