Personal names may appear in Latin in various grammatical contexts. Normally, family names don't change, but given names (baptismal names) will change (or "decline") according to one of the 5 "DECLENSIONS" of nouns (but many personal names don't follow the rules!).
Many common personal names in Latin came originally from Greek names. This fact accounts for some of the irregular endings. Another complication is that personal names are frequently abbreviated in Latin texts. Usually the abbreviation consists of the first few letters of the name plus one or two letters at the end to give you a clue as to the grammatical case. Abbreviated names usually have some sort of long stroke over the name, but occasionally there will be no extra marks at all to tell you that the name is abbreviated. You just have to know that Johem, for example, is an abbreviation for Johannem, which is the accusative case of Johannes.
In records with genealogical content, names usually appear in predictable contexts: nominative case, if the name is the subject of a verb; genitive, in the context of child, parent, or relative of someone else; accusative, when following the preposition "inter" (meaning between, as in a marriage "inter Johannem Smith et Annam Jones"). Other grammatical cases are possible, because there are many ways to express relationships in Latin!
When you translate a Latin text, you can either use the modern name in the language of the country where the record came from, if you know it, or you can use the Latin nominative form of the personal name. When you enter the name into a genealogy database, it certainly does not make sense to use a "declined" form, such as Johannem, or an abbreviated form, such as Johem, as the name of the individual! If you asked someone who spoke Latin, "What is your name?" (Quid est nomen tibi?), he would always reply "Johannes" — or whatever the nominative form of his name was!
Here are some typical examples. When in doubt, check a site such as the Latin personal names page of the UK National Archives, or use Google to be sure you have the correct nominative form and the correct gender of the name!