Some staff insist on having the generational qualifier added to their first name. In your example, this would become John Jr Doe/My Company. They ask for this because a search by their surname, if it is a common surname, would give different results depending on how their account is named.
Another consideration is with how the generational qualifier is treated in other applications such as Active Directory or PeopleSoft. It would make sense to follow, when possible, the placement of the generational qualifier in these other applications.