But honestly I think a lot of the demon to Hecate equations were at the ideals of the group or person(s). Here's an interesting one for example I stumbled across. This presents Hekate as the mother of a particular demon that is being called upon and petitioned.
Salve Ducis Murmux! Agios Murmux Rex Mormolyceae!
[Hail Unto Murmux the Duke! Numinous (is) Murmux, the King over Ghouls]
Murmur Son of Hekate, I Call You Forth,
Ducal Archfiend and Eternal Daemon of Sciomancy
Depart from the Place of Your Dwelling
So that I Might Witness Your Greatness of Power
And Be Directed Aright by Your Clairvoyance and Discretion.
If This Place Has Become the Dwelling of Those Who Essay the Hinderance of My Progress or Would Predate Upon My Spirit, Or if I Have Constructed Egregores Which Would Enact My Detriment Wilfully or Otherwise,
I Ask That You Murder, Devour, Torture, and Slaughter
Each and Every Fucking One of Them.
Upon This Hour, Accept Them or It as My Sacrifice to You.
But if My Sovereignty is Unassailed by Foreign Spirits Tonight, Show Me that I am Safe by Pouring Power Through My Soul to Engender Evolution.
I Thank You Graciously for Your Protection,
Or for the Evolution Which Would Signal My Safety.
Liftoach Pandemonium, Et Germinet Mormo! Agios Murmux Rex Mormolyceae! Mormo Murmux Matthias-Daimon! Vefa Mena Murmur Ayer! Salve Ducis Murmux!
[Open the Infernal Plane, and Bring Forth Mormo! Numinous (is) Murmux the King over Ghouls! (Names of Mormo/Murmux)! (Demonic Enn for Murmur)! Hail Duke Murmux]
As I Have Spoken, So Let it Be Done.
https://vkjehannum.wordpress.com/catego ... ls/page/9/
There's a few interesting examples of Hekate / Hecate usage on the page, including gematria. Of note I neither endorse nor recommend the site simply use it as an example of various usages of Hecate / Hekate in practice. It is up to the individual practitioner / reader to determine the validity of the information or its usefulness to them.