Burt Jenner It's A Boy!

7/8/2016 2:52 PM PDT

Burt Jenner: It's A Boy!

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Caitlyn Jenner just scored another grandchild -- her oldest son, Burt Jenner, is a dad ... but someone beat him to the punch on handing down his name.

Bodhi Jenner was born Thursday weighing 9 lbs 4 oz. It's Burt and his GF Valerie Pitalo's first kid.

Burt tells TMZ it's family tradition for all male Jenner names to start with a "B" ... and he was planning to go with Burt Jr., but his gf's sister laid claim to Burton when she had a son. So, they went with plan B(odhi).

Burt and Valerie kept the birth low key -- we're told the only hospital visitors were Burt's stepdad and Valerie's BFF. Caitlyn hasn't met her grandson yet.