Tristan Thompson is in the throes of what could become a paternity dispute, but the newborn's mother isn't waiting for a judge to decide whether he's the daddy ... she's already given the baby his last name.

Maralee Nichols posted of photo of the baby, with the caption, "First came love, then came you ❤️ Angelou Kash Thompson."

Maralee went on to grouse that Tristan is not embracing the child, saying, "I want to thank everyone for your well wishes. Me and baby are doing great. Right now my heart and mind is on focusing on the baby right now. I am heartbroken that Angelou's father doesn't want to be in his life. I am hoping this lawsuit will bring us together and we can be a family."

It is interesting ... Maralee wrote, "First came love" ... clearly suggesting this was more than what Tristan has called it -- a one-night stand.

As we reported, Nicole claims the baby was conceived in Houston back in March ... around the time Tristan was in town to celebrate his 30th birthday. If she's right on the timeline, the baby was conceived when Tristan was still with Khloe Kardashian -- at least publicly they were together.

Nicole, who filed legal docs to establish paternity, claims she and Tristan were together for 5 months, and she also alleges he offered her $75,000 to stay mum on the baby ... with this threat -- he allegedly said he's retiring after this season and he will then become unemployed, so she'd get way less than the $75k he was offering.

She also claims, according to the Daily Mail, she had promised him a "birthday surprise" in Houston, which he knew meant birthday sex.

If this is indeed Tristan's baby, it would be child #3 for him.

Maralee is asking for child support and reimbursement for the medical expenses related to her pregnancy and birth.