I've recently seen some facetious replies to this perfectly serious question by people who obviously dismiss the whole story as a fiction. Wrong! Back in the 1970s I spent several years researching the identity of the Prodigal and privately published a book on the subject (Brussels, 1981, in French). There seemed to be several approaches to the problem, some starting at the family end (stories of exultant fathers, calves unexpectedly killed, jealous brothers etc., possibly legal documents relating to the original unconventional division of the property), others at the "far country" end (stories of extravagant strangers, records of itinerant Jewish labour). The problem is, of course, that the documentary record for any of this is very patchy. For example, I found a possible 882 pig breeding farms where the prodigal might have worked, but only 17 (SEVENTEEN) had any surviving labour records. However it as while examining some pig farming records in the National Archives of Syria that I found what I believed, and still believe, to be a possitive identification. Another resercher was working on prostitution at around the time of Jesus, and shared some notes with me. I was *thrilled* to discover that he had found a kind of diary kept by a prostitute called Lilia in Damascus (really a client record with comments). Several records referred to a Jewish stranger who had recently come to the area and was spending lavish sums of money on parties and women. Lilia seems to have been a little bit in love with him, and included more details than usual: she says he was short, but strong and aggressive-looking, and most importantly that "he had had his inheritance." She records his visits for 6 months, then he is mentioned no more. HOWEVER she mentions chronic food shortages just after the last reference to the Jewish stranger. These facts fit the Biblical account of the prodigal son so well that I think it 99.9% certain that it was him.
But his name? That's still a bit of a problem, as Lilia seldom referred to her clients directly by their names. And on only one occasion (in what remains of her "diary", which has several missing pages) did she actually refer to the Jewish stranger by name, and there, as bad luck would have it, the manuscript has been torn. The first part of his name can be read however, and it is "Ron...". There are several possible names of the period, all discussed in my book. As further information is unlikely to be forthcoming I suggest that we simply call the prodigal "Ron", though.
Your readers may be interested to know that I am now writing a book identifying the Good Samaritan. I hope to publish this in English, and possibly to make parts of it available on the internet. There is still a huge amount of reasearch to be done identifying the persons in the parables.