I was named after my father who was named after his father, which
makes me the 3d or III.

My wife and I are expecting our first son this coming  winter.  
We have decided to give our son his own first name with a middle name
that shares both his grand father's name hyphenated.  With my last
name.

His full name ends with my name, for example.   Michael Jon-Joe Smith.
 If I am Joe Smith, III. Is it correct to name my son Michael Jon-Joe
Smith, IV?

Hi mxw7860-ga,

According to tradition, you only keep going with the numbers II, III,
IV, V, VI, etc, when the child has the exact same name as the relative
prior. You COULD do anything you wanted, there isn't a law about this,
but tradition dictates it to be the EXACT same name.

"If your name is John Henry Doe and you name your son John Henry Doe,
you then become Senior (Sr.) and your son Junior (Jr.)... If your son
John Henry Doe, Jr. names his son (your grandson) the same, his son
then becomes ?the third"?, i.e. John Henry Doe III."

If this answer requires further explanation, please request
clarification before rating it, and I'll be happy to look into this
further.

Nenna-GA
Google Answers Researcher

Thank-you.  I was unclear about the tradition and I don't want to make
any mistakes with my first child's name.

I appreciate the effort, your service is great.

I am sure my wife thanks you too.  :)

Legally you can, of course, name your son anything you please, and
append any Roman numerals of your choice. By tradition, however, your
son would be called "the Fourth" or "IV" only if his full name were
identical to yours.

Some of this material may be of interest to you:

http://www.answers.google.com/answers/threadview?id=385889

Thanks for the compliment, I'm glad I could be of help :) Good luck
with the upcoming birth!

Nenna-GA