The socialite was glowing in new IG pics Friday ... finally showing off baby London to the world, while sharing she’s always dreamed of having a girl to name after the British capital -- keeping it all in the family with the city-themed names like hers and her son, Phoenix.

Paris is in the full swing of motherhood, writing in her caption, "I'm so grateful she is here. I truly cherish every moment I spend with her. Together with Phoenix, my angel babies have shown me a love that I never even knew could run so deep before I became their mother."

Paris has always been a social media queen, quickly introducing her son Phoenix to her followers right after he arrived ... even though some people weren't so nice in the reception.

With London, Paris kept things closer to the vest for longer ... the cautious approach likely stems from the harsh comments social media trolls made about her son Phoenix's head size.

Paris was quick to slam the bullying ... saying "targeting my child, or anyone else's for that matter, is unacceptable." With that history, it's understandable why she might've been hesitant to show off her girl ... but people were kinda demanding it on social media regardless.