You are right, you can use Chloe, William, or Jana for a Muslim baby. Islam doesn't contain any rules regarding names, but the Prophet, peace and blessings of God upon him, is known to have disliked names with negative meanings, such as Harb (Arabic for "war").
In Iran, even though the majority of its people are Muslim, they use many names taken from Pahlavi origins, whose religion was the pre-Islamic Zoroastrianism religion.
In Kurdistan, the Kurds, even though 99% of them are Muslim, they name most of their children names that come from Kurdish, Greek, Russian, and other cultures, rather than from Arabic/Islamic origins.
Most scholars would recommend that you use an Islamic name so that your children would have "a stronger Muslim identity". But names aren't a big deal in Islam, and for the most part you can use whatever name is easy to use in your culture, and there are very good reasons as well for using Western-style names. A person with a Western name will have a better chance at bringing the understanding and acceptance of Islam to the West, and will be able to live and interact less problematically with the people.
The scholars in, say, Saudi, would be shocked if a Saudi couple named their children "Joshua", because this is an obvious breaking away from the Arab/Islamic culture of Saudi. But in Kurdistan, Iran, or Turkey, they have successfully embraced Islam without having to give up their culture. There is no reason why people in the West can't do the same thing. Nobody complains about a Muslim Kurd naming his/her child Kawa (Kaveh in Persian), who is a pre-Islamic mythical hero. A British person has the same right to name his/her child Arthur, after King Arthur.
Thus Islam gives you the freedom to use Christian and Jewish names, it all comes down to cultural considerations. Using a Christian name in Saudi may not work so well, but in Germany it may even lead to better results for the child compared to using an Arabic name.
You may find people who will make a big deal out of names. But for cultures that embraced Islam early, such as the Kurds, Persians, or Turks, even though the vast majority of their populations are Muslim, they never make it an issue what name you choose for your baby, and both Islamic and non-Islamic names are equally accepted.
The Prophet himself, peace and blessings of Allah upon him, had a Coptic wife who came from the Christian culture of Egypt and whose name was Maria, and he didn't ask her to change her name.