There are several plausible reasons for being "named" incorrectly when your Compostela is issued. Many of the issues can be corrected by attention to detail and proper case usage. So, some of the posters above are correct.
However, I witnessed two entirely different scenarios while working as an Amigo last summer.
The first scenario is where an American pilgrim had a given name that literally had no Latin translation. So, the person writing the Compostela was compelled to use his actual given name. This happens fairly regularly, as contemporary names are sometimes "creative" and without historical basis that would equate to a Latin derivative. It can also occur, when a pilgrim is from a non-Judeo-Christian culture, and has a name that has no Latin equivalent.
The second scenario is where a pilgrim reacts vehemently to the Latin version of their name. Last summer, one German woman, upon seeing that the name on her passport had been translated into it's Latin equivalent, became very agitated declaring to me that "no one has that name...all the people with that name are ugly, old, and have hairy moles...!" Ok, no problem. I advised the young lady to return immediately to the employee who had written her Compostela, and to insert herself after he/she completed the transaction they were now working on. I suggested she tell the office employee that the name indicated was unacceptable and that she preferred the name on her national passport...problem solved...another satisfied pilgrim...
When I am working the sometimes long queues before people get into the pilgrim office, I regularly tell people to pay attention to the Latin variant of their name that the employee writing Compostela proposes. If they have an issue, THAT is the best time to comment or request and alternative - BEFORE the Compostela is written. I usually recommend they go with the same name as is on their national passport or EU1000 card. I explain that, on my first Camino, and not knowing any better, I came home with my gender changed...
The chap writing my Compostela had the correct name, but got the gender wrong. We got that sorted on my next Camino. But my mother was NOT pleased....
So, the bottom line, is for pilgrims to remain part of the Compostela process, pay attention and POLITELY speak up if you disagree.
I hope this helps.