Asalaamu Alaikum, A convert to Islam is not obliged to change their name to a muslim name. However, if the non-muslim name has a meaning that is against Islam then selecting a new name would be advisable.
Nabi (sallallah alayhi wa sallam) has mentioned that we will be called by our names and by the names of our fathers on the day of judgement, so we must keep good names. In another hadeeth it is narrated that Nabi (sallallah alayhi wa sallam) use to change those names that were bad. In yet another hadeeth we learn that Nabi (sallallah alayhi wa sallam) use to change those name that had a bad meaning. Nabi (sallallah alayhi wa sallam) personally changed names that had a bad meaning. In light of the above hadeeth we learn that it is of utmost importance that we name our children with good names that have a good meaniing. Also ones name should identify one as a Muslim.
In regards to the naming of children:
It is preferred by the shari'ah that the father or the grandfather in the absence of the latter decides on an honourable and beautiful name for the newborn. The Prophet (May Allah bless him and give him peace) said: ((Verily you will be called on the day of resurrection by your names and the names of your fathers so beautify thy names.)) Abu Dawood. It is sunnah to name a child on the seventh day of its birth before one carries out the 'aqiqah.
The best names as the prophet (May Allah bless him and give him peace) has indicated in a sound hadeeth in Sahih Muslim is, 'Abdullah and 'Abdurrahman, and names similar to it starting with the word 'Abd (slave) such as 'Abdulkhaliq and 'Abdurrazaq and so on. It is also permissible and highly recommended to choose a name from amongst the beautiful names of the Prophets such as Musa and that of the Angles such as Jibreel and Mikaeel (Peace and blessings upon all of them). Our prophet (Sallallahu Alaihi Wasallam) said: ((Name your children by the names of the Prophets'.)) Abu Dawood, Nasai and others. In another tradition our Prophet (Peace and blessings upon him) said: ((Who so ever names his child Muhammad out of love for me and to attain the barakah there from, he and his child will be in Paradise.)) Musnad Imam Ahmad and others. According to Imam Al Suyuti this hadeeth meets the conditions of a hassan hadeeth.
Then it is makruh (offensive) and disliked by the shari'ah to choose an ugly name for ones child such as, Murrah (bitter), Harb (war) and names of other religions such as Susan, Sonya, Jack etc. It is haram (prohibited) to choose names which Allah alone is known by such as Malik al Muluk which means King of Kings or Al Kabir (the Great One) or Al Hakim (The Wise One or the Law Giver).
A man once came to the Prophet (Sallallahu Alaihi Wasallam) called Abu Hakam. The prophet (Sallallahu Alaihi Wasallam) said onto him: 'Allah is Al Hakim, what do you have of children?' The man replied: 'Suraij, Muslim and 'Adullah.' The prophet (Sallallahu Alaihi Wasallam) then asked him: 'Who is the oldest of them?' The man replied: 'Suraij.' The Prophet (Sallallahu Alaihi Wasallam) then said: 'You are then Abu Suraij' Abu Dawood.
Finally naming a child Hakim without the particle 'Al' attached to it is acceptable, though the name �Abdul Hakim far accedes the merit of the latter.
And Allah alone knows best.