Praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
Since the name (Dalaa`) is causing a great deal of embarrassment to the above questioner and his family, then it is permissible to change it into another suitable name since the Messenger of Allah used to change bad names to good ones. Narrated AbudDarda': The Prophet (Peace be upon him) said: "On the Day of Resurrection you will be called by your names and by your father's names, so give yourselves good names." {Related by Abu Dawoud}.
In conclusion, we recommend responding to the questioner`s request by changing the name of his daughter in consideration for his and his family`s feelings. And Allah The Almighty Knows Best.