In the first place, we would like to stress that there is no specific injunction that requires a person to change his name after accepting Islam. The vast majority of the Prophet’s companions (may Allah be pleased with them all) did not change their names after accepting Islam. However, it is recommended if a name contradicts Islamic principles or values it should be changed to a better-meaning name. For example, the Prophet (peace be upon him) advised one of the companions, whose name was “Harb” which means “war” in English, to change his name to a better-meaning name.
It is not absolutely necessary for you to change your name if you are converting to Islam as long as your name does not have any taint of shirk, or as long as it does not suggest ideas that are repugnant to Islam.
If your name, however, contains or implies shirk (associating partners with Allah) as is the case with names such as servant of Muhammad, servant of Jesus, servant of Abraham, servant of Ka`bah, and so on, you must change them.
Abu Bakr, the first caliph of Islam, and the Prophet’s closest companion, before his conversion to Islam, was called `Abd al-Ka`bah (servant of the Ka`bah) and the Prophet (peace be upon him) changed his name to `Abdullah (servant of Allah).
Likewise, if your name contains ideas that are repugnant to Islam, then again, you ought to change it; hence the Prophet (peace be upon him) changed or objected to names suggesting unsavory ideas such as Flame of Fire, War, Bitter, Hard to deal with, King of kings, and so on. He also discouraged names implying: prosperity, success, profit-making, and so on; forbearers of these names may likely be taunted for not living up to their names. The Prophet (peace be upon him) loved names such as peaceful, lenient, gracious, noble, bearer of good news, fair, pure, and so on.
While prohibiting or discouraging people from naming with the above names, the Prophet (peace be upon him) encouraged them to use names that have good meanings or are inspirational; thus he loved names that are indicative of servitude to Allah (as is the case with names like `Abdullah (servant of Allah) or `Abd al-Rahman (servant of the Beneficent); he also loved naming children after the true role models of humanity such as prophets and righteous people. So he called his son Ibrahim.
Once the above considerations are taken into account, there is nothing wrong in keeping the previous name, as one is not obligated to change his/her name in order to become a Muslim.
In conclusion, in the Western context, names such as Devil’s angel, Wolf, and so on, are considered un-Islamic.