Kim and Kanye -- Name Your Baby ... Or Else!

Kim and Kanye's kid is now 3 days old, and still no name ... TMZ has learned.

Our Kardashian sources tell us, they just can't come up with a name they feel is a keeper. We're told they've narrowed it down to "a few," but they haven't settled on one.

As for why the delay ... we're told Kim's in a lot of pain. It was a difficult birth because of her condition -- placenta accreta.

Turns out the clock is ticking ... the folks at Cedars-Sinai Medical Center tell us, parents MUST name their child within 5 days of birth, counting the day the bambino is born. And, we're told they will not discharge the mother before a name is selected.

So for Kim to leave, she has to come up with a temporary name, which they can change at a later date.