Poor baby, he'll probably get a name change and then later another name change when they find out
he's Eric's son.
It will be interesting to see if EJ and Nicole learn that "their" son is alive and is baby Jude, if they will change his name.
Bo and Hope slightly changed "Isaac's" name to Beauregard Isaac Theo Brady, but called him Zack. (Lexie and Abe named him Isaac Theo Carver)
Glenn and Barb Reiber left their son's name as John Thomas, still calling him JT, as Bo and Hope did. (they actually slightly changed his full name to John Thomas Brady Reiber)
Sami left Sydney's name as is (Sydney Anne), which is surprising. You'd think she would've wanted to rename her baby since Nicole picked out Sydney's name.
Philip didn't change Parker's name after finding out that was his son, but then they switched it again to say Daniel really was Parker's bio dad, so all was good (Parker was Daniel's mother's maiden name).
Abby changed "Colin's" name to Thomas Jack after she got out of the burning cabin and the baby was found and brought to the hospital. Chad gave Thomas the last name Deveraux on his birth certificate, saying he'd probably have an easier time in Salem without the DiMera name. But I guess the writers have forgotten that.
Brady and Jeannie T changed "Christopher's" name to Tate. They said if he had been a girl, they'd have named her Melanie, since she's the one who figured out Kristen's baby was really theirs and reunited them. There was some comment about how Tate meant cheerful and happiness, and that's what Melanie brought to their lives by reuniting them with their baby.
Brady and Kristen changed "Mackenzie/Mickey's" name to Rachel Isabella, the name they gave to their "deceased" baby, after both of their late mothers.
Billie named her "stillborn" baby Georgia. But the adoptive parents who raised her named her Chelsea. In that case though, she was a teenager who had the name Chelsea all those years, before the truth came out.