Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear sister, we would like to thank you for your very interesting question as well as the great confidence you place in us. We implore Allah Almighty to help us serve His cause and render our work for His Sake.
First of all, it is to be stated that there is nothing in the Islamic sources to indicate that a new Muslim is not allowed to keep his original name unless it carries any meaning contradicting Islam and its beliefs. Since Islam is a universal religion, there is no such requirement. However, it is preferable to carry a new name that signals one's entrance into Islam. Likewise, there is nothing wrong in carrying a compound name, so that one may keep his or her old name with an Islamic name added. The laws regarding name changes vary from country to country, so that one might also choose to keep his or her old name as the legal name, but use the Islamic name among family, friends, and colleagues.
In response to the question you raised, the European Council for Fatwa and Research issued the following Fatwa:
There is no legal objection to carrying a compound name, so that one may keep his or her old name before he/she embraced Islam with an Islamic name added. The ways and tradition of the Arabs was for each person, and particularly those of elite stature, to have a name, surname and nickname. For example: `Abdullah, Abu Bakr, and As-Siddiq (all referring to one person), or `Umar, Abu Hafs, and Al-Faruq (all referring to another person). Islam approved of all these names and agnomens.
Therefore, we find no objection to a person, whether man or woman, carrying two names which he or she is known by, particularly one who embraces Islam and wants to keep his original name, on condition that the name does not carry any meaning that contradicts Islam, such as "`Abdul Masih" for instance. Indeed, one may keep his or her original name without changing it if its meaning does not contradict Islam, as the companions all kept their original names after they embraced Islam, although it is preferable to carry a new name that signals one's entrance into Islam.
The Prophet Muhammad (peace and blessings be upon him) liked the names that carried beautiful meanings, and he (peace and blessings be upon him) disliked the names that carried bad ones. In such cases he would choose a better name for the person, such as the case when he (peace and blessings be upon him) changed the name of a woman from "`Asiyah" (sinner) to "Jamilah" (beautiful).
The Prophet (peace and blessings be upon him) stated: "The best of names are `Abdullah and `Abdur-Rahman, the most truthful of names are Harith and Humam, and the worst of names are Harb and Murra."