Religion
Howard did not write much about Derketo, but what he did write actually does some very heavy lifting. Although one would have liked to have a little more definition, but due to the nature of Howards works being pulp, then I would say we have enough to extrapolate.
Queen of the Black Coast
"But the gods are real. And above all are the gods of the Shemites — Ishtar and Ashtoreth and Derketo and Adonis." - Belit
This quote places Derketo plainly with the gods of the Shemites.
The Slithering Shadow
"I am a daughter of Luxur, and before I had known fifteen summers I had been led through the temples of Derketo, the dusky goddess, and had been initiated into the mysteries. Not that my first years in Xuthal were years of unmodified pleasure! The people of Xuthal have forgotten more than the priestesses of Derketo ever dreamed. They live only for sensual joys. Dreaming or waking, their live*s are filled with exotic ecstasies, beyond the ken of ordinary men." - Thalis the Stygian
This is probably one of the most telling quotes about what Howard intended with the domains that Derketo encompasses, most certainly one, but we could extrapolate more from this as well. Firstly this quote evidently points to Derketo being a god of sexuality and desire. The mention of the temple of Derketo and being led through it is not conclusive but the way it is framed by the quote after is what defines it. That being said, we could further say, fertility and life are also present in this concept, or desire and vice.
Red Nails
"That's what the black people of Kush call the Apples of Derketa. Derketa is the Queen of the Dead. Drink a little of the juice, or spill it on your flesh, and you'd be dead before you could tumble to the foot of this crag." - Conan
So is rather conclusive as well, and almost contradicts what we extrapolated from Thalis’ quote. Notice that the spelling is different, let's assume this is not a spelling mistake since this is the only occurrence of this spelling, and assume it's intentional. Kush is much further south, we know concepts of the same God deviate over distance and culture so it would not be hard to imagine a duality to Derketo based on region. Queen of the Dead is a very telling title. But life and death, fertility and decay are usually paired together in symbiosis, this is probably where later pastiche writers made their case for their own conceptions.
Black Colossus
"By Derketo, Conan, I am a prince of liars, but I do not lie to an old comrade." - Shemite informant
This points to those of questionable morals and ethics swearing by Derketo, but also they are Shemite, which further solidifies that Derketo is a Shemtish God.
Teeth of Gwahlur
"They would be placed in the temple of Zembabwei beside the squat gold idols of Dagon and Derketo, sacred guests in the holy shrine of the kingdom." - Narrator
"Give the Teeth of Gwahlur into the hands of Thutmekri, the Stygian, to place in the sanctuary of Dagon and Derketo." - False oracle
Now this is interesting, Howard only ever mentions the god Dagon, in name only, there are many that think it's a nod to Howard’s long term friendship with HP. Lovecraft. Which makes sense. What we can glean from this quote though is that Derketo is not a lone god, she can and has been included in paired worship, which tracks with how Howard presents the Shemite gods.
The above are the only places Derketo/Derketa are mentioned in Howard’s original works, and it truly outlines how much pastiche writers have taken creative license. Conclusively the only thing we can pin to Derketo is that she was a Shemite Goddess of sexuality, and we can loosely assign concepts of fertility by extension, if not fertility then desire and taking pleasure in the vices of life, or perhaps all of the above.
Of course if we include the works of Funcom, and specifically Conan Exiles, they have expanded Derketo into two domains, the northern cult, that aligns more with the Stygian concepts of excess, subjugation and pleasure and then the southern cult, which assigns to her the domains of death and decay. Both of these are actually extrapolation’s of Howard’s original work. In reference to Thalis, and then what Conan says about Derketa’s apples in Red Nails.
How much you should take from Funcoms work and later pastiche writers is up to you, but they do not define a conclusive image of what Derketo is about. Only a creative take using Howard's work as a loose base.