Prince William, Kate Middleton Welcome New Daughter Whatever Your Name Is

5/2/2015 8:10 AM PDT

William and Kate's New Daughter -- Welcome, Whatever Your Name Is (VIDEO)

Kate Middleton bounced back hours after giving birth to a little girl who is now 4th in line to become England's head honcho, thanks to Prince William.

The third in line to the throne briefly left the hospital Saturday where his wife, Kate Middleton, gave birth to the 8 lb. 3 oz. baby.  William returned 10 minutes later with 1-year-old George.

Daughter and mom are doing great, and William -- who was present during the birth -- did not look the worse for wear.

The baby -- whose name has not been announced -- is now 4th in line for the throne, behind Charles, William and George ... and 5th if you count Tommen Baratheon.

 BTW ... the Queen dressed in pink Saturday for an event.  It's unclear if she had a blue dress just in case, or whether she was clued in ahead of time.