The Pilgrim Office has a table in their computer database. I believe this table was constructed from historical sources, writings, and older Latin dictionaries. When you present your credencial, they take the first name (given name) shown and refer to the alphabetical search results.
For example, a search for "Betty" will likely bring up entries for Elizabetham, Beatriciam, etc. Usually, several alternative Latin variants are presented. Women's names always end in '...am.' Male given names always end in '...um.'
NO, I do not know why this is the case. Perhaps a Latin scholar in the Forum might care to elaborate. But, I surmise it is to clearly flag male from female given names. The Bible is very binary in this regard. You have to be one or the other, because the Book of Genesis says so...
As Latin is officially a 'dead language' this infers that no additions are being made. But some things are still open to interpretation. For example, the given name Todd, might be derivative of Thaddeus, Theodore, or simply "Todd." Clearly, there are no "Todds" in the Bible, toads yes, but Todds, no.
I have seen this issue before. When a pilgrim named "Todd" presented himself, we asked if he was baptised or christened a Christian (any Christian sect). He said yes. We said, "...okay, if your parents were given a certificate to formally commemorate this ceremony, what name was on that certificate?" The reply was 'Todd." Hence, this is the name placed on his Compostela.
In cases of dispute, the office will generally accede to writing down the name you insist on. So, highly secular names, not derived from a Latin name, are permitted...
Hope this helps.
One can only try...