A Kohen is not allowed, from a halachic perspective, to marry a convert to Judaism. It turns out that not everyone named "Cohen" is a kohen, though it is pretty common that they are. David Cone, the former Cy Young pitcher, for example, is not even Jewish, let alone a kohen, though he spells the name differently.

Anyways, a fellow named Cohen went into the Rabbanut of Ashdod to register his upcoming marriage to a convert. The beis din obviously looked at the paperwork and the marriage license of his parents and said "no way" - a kohen is not allowed to marry a convert!

Mr Cohen responded that despite his name, he is not a kohen, his dead father had not been a kohen, and his grandfather had not been a kohen. That reminds me of a joke.

Mr Cohen claimed that he had been raised by his grandmother. When she and her son, his father, moved to Israel, she registered their names using her maiden name "Cohen", even though their family name was no longer Cohen but something else. So, grandma was from a line of kohanim, but dad was not.

Throwing a wrench into this was Mr Cohen's brother who admitted that for a period of time he had performed the priestly blessings and taken the first aliyah to the Torah as a kohen, but that was because at the time he had assumed he was a kohen based on the name. He says he stopped when he discovered otherwise. The beis din confirmed this with the gabbai of the brother's shul. Further throwing a wrench into the investigation was the discovery that the brother had tried to marry a divorcee, making the same claim about not really being a kohen despite the name, but the beis din in Tel Aviv did not allow him to.

The beis din in Ashdod got the family records from the Ministry of Interior. This only made it more difficult as the beis din discovered that various family members, including Mr Cohen and Mr Cohen's father, had changed their names a number of times over the years, both first and last names.

A thorough investigation had the beis din accessing old records in Tunisia. There they somehow discovered that the real grandfather of Mr Cohen was not a kohen, though he is not the grandfather listed as Mr Cohen in the grandmother's ketuba. Further investigation revealed some older records in Tunisia.

It seems to be very confusing but it turns out the grandma Cohen is really the father's grandmother, and Mr Cohen's great-grandmother. Great grandma Cohen had been married to a non-kohen and they had a daughter - the mother of Papa Cohen and grandmother of Mr Cohen. Her husband died and she remarried to a Mr Cohen, that was a kohen. When they moved to Israel, she took her grandson with them and registered him as their son, using her current name, Cohen.

At the end of the investigation and halachic debate over the matter, the beis din decided to pasken that Mr Cohen is allowed to marry the convert he wished to, while adding a prayer that God should save them from a mistake about this.
source: Kikar and Kipa

I am impressed that the beis din was able to piece it all together and figure out a complicated situation like that. Perhaps more impressive is that they went through the effort and did not just stop at any point in the middle and just prevent the marriage from happening.

Mazel tov!