Frankly, all said, I think the Michael Kyle Stone Jr. combination should go only to the child of the woman he married.
Has the first woman's baby been born yet? If so and he has not gotten a DNA test done yet, he should!!! And he should not sign the birth certificate until he knows for sure he is the dad (and, of course, he should sign it if he is). It's pretty clear-cut. If the first woman's baby is not his, then she has no business naming the baby after him, certainly not to the level of the middle name being the same and a Jr. attached. If she likes him, she could name her baby in his honor, but the Jr. stuff is just a lie if the baby is not from him. This is true even if he has promised her moral support in the future whether or not the baby is his.
If the baby does prove to be his by DNA test, he should only name the baby his full name and Jr. if he intends to be a very active dad in the baby's life. If he is just going to pay child support and have alternate-weekend visitation, sorry, he can't go labelling the kid as though he is a doting daddy.
If he does intend to be a very active dad, and if the DNA test proves the kid is his, then he can name the baby his name and Jr. if he wants, but frankly if it would cause trouble in his family with his wife who is pregnant, I wonder why he would.
I really don't recommend having two kids in the same area being named the same name with the only exception being a Jr. and a III. They are going to grow up getting each other's mail, and getting their grade reports confused by the school district, and like that. You wouldn't name two siblings the same name (with the exception of George Foreman, who is not a role model for intelligent thought). Just too confusing in life.
So, this means -- if the first baby gets the Jr., the second baby should get a different name, maybe after the wife's dad, since the man she is married is not getting how she feels.
Any suggestion on the name
Wait it my be confusing hold on baby #1 is not from the woman he married