I really love and appreciate, at the same time that I see the irony, that most of Maul more healthy or that he respects relationships are with woman rather than with men.
Denine (the Droid that raises him) is usually referred to as she/her or just it, and despite the problems, he comes to value her as an important aspect of his life and has mixed feelings on her destruction.
His first friend is Killindi Matako, a nautolan girl who freed herself from slavement, he respects and likes her a lot, even being protective of her and being able to work together perfectly when needed. They were so close that in the scene that Maul comes back to Orsis to finish everyone, he finds her in the principal offices fighting with her own guardian and a teacher because he has disappeared, she's smiles at him despite being scared when he goes to kill her and he is forever hunted by her.
Daleen is the third in the friend group and just has little screen time, but in this time she hugs and leans on him and it clearly shows that he is used to it, making her one of the few people that is to touchy with him, while also making part of the surprise Killindi wanted to show him too. When he founds her sleeping in her room with Killindi, he is glad that he can make it quick and painless, and thats how he kill her.
Eldra Kaitis, the first jedi he kills, is a padawan with who he fights side by side and tries to convince him that it doesn't have to end like this and save him, he recognizes her talents and respects her as a jedi and almost trusts her, he still remembers her years later and thinks about her.
He easily accepts Qi'ra as his second in command, respects her and even teachs her a fighting form to kill sith, trusting she wouldn't use it against him. Also leaving the criminal empire he passes years building in her hands.
He refers to Satine as striking and admirable, he wouldn't have killed her if it weren't for her connection with Obi-Wan, he would see her as much more useful and important than that.
He respects Ashoka more than he ever did respect Obi-Wan and more than he would even respect Anakin. He sees their teachings in her but also recognizes her as her own self strong fighter and jedi. He believes that together the two of them can actually take down Sidious and opens up to her like he never did for anyone else to convince her, even in the fight after she refuses he never tries to kill her, more like stalling so he can leave and thats what gets him locked up and even then he never stops referring to her as lady Tano because of the respect he feels for her.
Rook Kast, his second in command is a fierce mandalorian woman who he trusts completely and is extremely loyal to him.
His mother, all things considered, is still one of the few people we see him grieve and he suffer a lot for her death for him.
And now in his new series, his apprentice is a twi'lek girl (will give him Eldra flashbacks a 100%) who he will most likely come to care for a lot for and teach the best he can.
In comparison to the men in his life, the more important one is by far Savage and no other come as close in levels of trust and care Maul has for.