I am sure every Muslim believes that Allah(SWT) is the only eternal supreme Being. Given that, I have heard, from Muslim scholars, that it's not appropriate to give children names that might show similarity to the attributes of Allah.
That said, Khalid, a popular Arabic name(Khalid Ibn Al-Waleed: A companion of the Prophet(PBUH)), which means immortal or eternal, seems to be widespread across the Islamic world. I wonder if the properly-Islamic-naming principle applies to this name.