Family Ties: Junior, Senior, III, Etc.
Some folks believe that the highest honor you can bestow on another person is to name a newborn baby after him or her. Juniors, IIIs and IVs are done much more often with male babies, though many female children have either a first or middle name that comes with family history attached.
Although this naming convention can create a great sense of pride for a family, it can also be a problem when Junior grows up. For one thing, it can create more red tape for government and credit-reporting agencies, as they often confuse one family member's name for another, sometimes with disastrous results. It can also result in mixed-up mail once Junior is out on his own.
But more than that, you need to realize that you could be inadvertently forcing baby to live up to his father's accomplishments instead of allowing him an opportunity to develop his own identity in the world. So, choose carefully!
If you are absolutely set on successive naming, note that it is customary to use Jr. when the son is second in line, and Roman numerals for each successive child in the lineage. If baby is the fourth James Smith, his name would read James Smith IV.