This is really powerful magic, and rare to create entities out of nothing. Sometimes they appear as the group has imagined, sometimes disturbance in shared imagination might make these entities slightly different than ment to be, or even dangerously out of control.
Usually it needs a group to create an entity this way, but very powerful mages can also create one themselves. They don't necessarily have differences of mind in creation process what group brings, but when the entity born, it might be hard to control alone.
Similarly cults or religions might create new gods. Of course, gods are powerful, so they need much energy and belief to be formed. This needs a great group of believers of cultists or religionists. Sometimes, gods are formed out of despair or need. Sometimes one man has this idea of what he wants to create, and needs followers with faith into his word to finish his idea into an actual entity.
Some do create via belief gods in need. For good things. But some, usually cult leaders with selfish needs do want to create gods for their own purposes. It might be obvious for cultists that the god will be evil (or is if cult leader has told so already even if there is nothing existing yet) or the cult or religion leader might masquerade the god to be good and only harvests the power of the belief trying to shape it as he pleases to create an evil god despite of his believers' belief.
What if no one believes in a god no more, what was created by group belief? The god dies. The god might be true, and he might have followers, but some powerful institute what doesn't like that god, might start persecution against the believers. As they hunt down the believers and kill them, for a moment the god might be more powerful than ever as the remaining and hunted followers might believe in him more. But as time passes, and people are killed and persecuted, the power of belief starts to fade. Because of the lack of believers left, or more damagingly because of those who rebound their faith in fear of death.
If there are only few left, the god is sleeping. It is alive, as long as there are those who believe, but the god has lost his power. It is sleeping (hybernating). This is when usually cults are formed. The god is long forgotten, nearly unexistent, and secret cults are formed with carefully chosen members who are guaranteed to advance the awakening of their god.
For high fantasy setting, several lesser deities can easily be explained by this. It also can explain various evil cults. In modern games, I wouldn't necessarily go as further as creating gods, but maybe beings. In horror campaign these artifically with imagination created entities could very well be demons.
Also in Call of Cthulhu games sleeping gods and secret cults could be explained this way.
Here are a couple of articles, that were inspiration for this idea. The Philip Experiment.
"In the 1970's, a group of Canadian parapsychologists wanted to attempt an experiment to create aghost, proving their theory that the human mind can produce spirits through expectation, imagination and visualization.
The actual experiment took place in Toronto, Canada, in 1972, under the direction of the world-renown expert on poltergeists, Dr A. R. G. Owen.
The members of the experiment proposed an idea... by using extreme and prolonged concentration, they could create their ghost through a collective thought form: Non-physical entities which exist in either the mental or astral plane. In order to create this ghost and make it as 'real' as possible, it needed a life story; a background in which the ghost could 'relate' to."
Quote from first link to sum up The Philip Experiment.