As salaam alaikum.
It is according to sunnah, to change a bad name immediately, and it is permissible according to sunnah to exchange a name for a better one.
The Prophet used to change a bad name. (Al-Tirmidhi #4774)
Narrated Abu Huraira:
Zainab's original name was "Barrah," but it was said, "By that she is giving herself the prestige of piety." So the Prophet changed her name to Zainab. (Sahih Al-Bukhari 8.212)
If something is not classified as haram within our deen, then it is permitted. Retaining a name that does not identify itself with anything Islamically forbidden and is not a Name of Allah (swt), has not been declared haram. So the question then is the name 'Dolly' haram?
Dolly is a pet form of the english name Dorothy. A common Christian name after the life of Saint Dorothy of Caesarea (http://saints.sqpn.com/ncd02823.htm
). As the patroness of brewers
and strongly Roman Catholic in logos and meaning I question whether the name is lawful.
It is reported that the Prophet (saws) said: "On the Day of Resurrection, you will be called by your names and by your fathers' names, so give yourselves good names." (Hadith Abu Dawud)
Allah (swt) knows best.