All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
First of all, we thank and praise Allaah Who guided you to Islam and we ask Him to make you firm and steadfast on His Religion until the Day you meet Him.
As regards your question, you are not Islamically obliged to tell the man who wants to marry your daughter or his family that she was born out of wedlock.
If the marriage takes place while fulfilling the conditions of a correct marriage – the most important of which are the presence of the guardian and the presence of two trustworthy witnesses – then the marriage is valid. What you mentioned in the question does not affect the validity of the marriage. For more benefit on the conditions of a correct marriage contract, please refer to Fatwa 83629.
It should be noted that if a Muslim woman does not have a Muslim guardian, then it is the Muslim judge or his deputy who marries her off. If none of them is available, then she appoints a Muslim man to marry her off. Ibn Qudaamah said (in Al-Mughni): “If a Muslim woman has no guardian and there is no Muslim ruler, then according to Imaam Ahmad Ibn Hanbal, there is evidence which proves that a just and trustworthy Muslim man may marry her off with her permission.”
It should be noted also that according to the view of the majority of the jurists a daughter born out of wedlock should be traced back to her mother and she should not be traced back to the Zaani (the man who committed fornication or adultery with her mother) but some jurists are of the opinion that if the fornicator or adulterer asks that she be traced back to him, then she is traced back to him as already clarified in Fatwa 143587.
In the above Fatwa we clarified that if the time of the daughter's marriage is due, she can be given a general surname other than that of her mother in order to avoid any embarrassment according to the view of the majority of the scholars who consider that it is not permissible to trace her back to the fornicator/adulterer.
Allaah Knows best.