Is the answer
People, demons, deities——
These three love to follow me.
Pan's People; Pan (demon and god/deity figure).
Starving, penniless——where reside thee?
I may satiate or be half your need
You can use pans to cook food (if you are starving), and there is also a thing called gold panning to find gold (if you are penniless).
Since you used the archaic word "thee" then I will use the archaic definition of "satiate" which is to be satisfied to the full. Talking about starving, when people are full, it usually means they have eaten and are not hungry anymore; they are satisfied.
Of course, if you want food, you can look in the pantry, for which half that word is "pan".
Edit: Thanks to @stuartstevenson, the French annunciation of "pain" is "pan", and "pain" means "bread". This part is important particularly for the following sandbox, but also it ties in to Jesus Christ's command that "man shall not live by bread alone, ..." when Jesus was fastening and poor (starving and penniless) during his temptation from Satan (here).
Edit: You can use regular pans to fry eggs and satisfy your hunger, referring to "starving", and to panhandle means to beg on the street, which would refer to being "penniless". Panhandle is a compound word made up of pan and handle, so I guess pan is half of the entire word in the context of it being compound.
Cupboards, crumbs, committees——
Those are different yet still come with me.
Cupboards and crumbs are once again involved with the pantry or just normal pans. There is a thing called pan-regions which might involve committees. Pantries, pans, and pan-regions are all different.
Edit: Perhaps it could be referring to pan racks for "cupboards", regular pans for "crumbs", and the Pan-African Parliament for "committees".
Always carousing, happy and merry;
Yet wake me up and you may see:
Always carousing can cause a pandemonium, and someone who is happy and merry (especially because he never grows up) is a familiar guy called Peter Pan.
Disaster, alarm, anxiety——
All those come out when I shriek.
Well, a pandemonium can cause a disaster, anxiety and be quite alarming. Also, when Peter Pan wakes up Wendy, and her brothers John and Michael, the parents are grief-stricken over their disappearance. The kids of course disappear when they fly out their home and shriek in the air towards Neverland.
Edit: thanks to @KateGregory: "pan pan" is what people on boats would say in the case of an emergency, a step down from saying "mayday" (here).
Say My Name Please
An anagram of say my name please is Me? Pan? Yes! Lame, say. Does this mean anything? Title is not a clue.
Louise Clark, the person who founded Pan's People, died at 63 of heart failure (coronary artery disease). And don't worry, the link will not contain a dead body.
Pan the demon and God were mainly apart of Roman and/or Greek mythology, which are languages. Pan's People was also a British dance troupe, so that language was English. But I can't fit the other clues.
PAN is $3$ letters long.
You can "pan out" with the $3$ words?