A candidate for conversion to Judaism appears to be very sincere, enthusiastic, knowledgeable, dedicated, and is not suspected of having ulterior motives. But he states that he does not intend to inform his family of his conversion. Is there anything in halacha that would prevent his acceptance?
I'm not seeing a black-and-white rule on this one, but any wise beit din (conversion panel) should look at the whole picture -- are we setting this person up for success? Are there any red flags here?
(How often does the candidate intend to interact with their non-Jewish family? How old/independent is everyone? What is their "game plan" for said interactions? When and if the family does find out, how are they likely to react, and what would the candidate then do?)
For example, the Rabbinical Council of America's Geirut Policies, Protocols, and Standards do includes this:
The Beit Din should also consider whether other significant individuals in the candidate’s life such as parents, or any existing minor children, will have an impact on the success or failure of the process and the aftermath of conversion.
Basically this is going to be a reasonable judgment call for the local rabbis.
As an issue of halacha apparently you don't have to.
If you did then we would be locking the door of conversion to anyone who grew up in a very anti-Semitic family.
The Midrash Tanchuma (Mishpatim 5) discusses the conversion of Onkeles, nephew of Roman emperor Hadrian.He did not inform there beforehand but used a ruse beforehand to avoid his wrath afterwards. He did tell them afterwards and Hadrian's advisors said to kill him.
Hadrian said not to kill him but according to l'havdil secular historians his memory was still expunged from the official Roman records. Hadrian's sister who is named as the mother of Onkeles in the Midrash officially had no sons. Or at least had none listed on the royal family records.
On a practical level however it is unlikely a Beis Din would agree to convert someone knowing they intend to keep it a secret from the family