Private Investigators are not officially held to customer confidentiality like a physician is, a good investigator may honor this. They should never talk about or provide any info and keep everything private that is shared between the two of you unless the investigator isn't happy in what you are telling him or how the investigation is shaping up the situation.
What is the first impression you have from that individual? What is his initial concern, the more money? (Your case should come first and then the money after you've decided you need to go ahead and employ the private investigator) Would you trust him?
If the investigator is compromised they should never disclose the customer's name, this will protect you from any consequences because of it. When hiring a private investigator you need to make sure that they have some experience in the field of investigations that you wish to perform.
Have they got any educational background such as; Police or military? How long are they employed as a Private Investigators have they completed any training classes? What areas do they specialize in? It's also good to ask if they have dealt with some other cases like yours earlier and what the end result was.