Cassie Gives Birth to Baby Girl Named Frankie

Cassie and her husband, Alex Fine, have welcomed their baby girl to the world ... and the little one boasts one of the coolest names ever.

Sources close to the situation tell TMZ ... Cassie gave birth Friday at an L.A. County hospital, and the couple named their first child Frankie -- Frankie Fine.

We're told their bundle of joy weighed in at 8 lbs., 4 oz and measured a smidge over 21 inches long.

As we've reported, Diddy's ex and Alex announced they were expecting in June, got engaged a couple months later ... then got hitched in Malibu in September.

If you recall ... there was some drama when the 2 began dating last year, because Alex was her former trainer. Any potential bad blood was washed away by the time they revealed their pregnancy news, though ... Diddy gave them a shout-out, wishing them nothing but love and happiness.

The well-wishes seem to be working. Congrats to Cassie, Alex and, of course, Frankie!!!