Does merely uttering the names of characters in games – which do not carry a meaning of disbelief but depict polytheism – lead one out of the fold of Islam, especially if there is no Sharia necessity for the name and with the belief in the falsehood of these beliefs? And does this ruling apply to the names of Greek gods like "Zeus"? And does disbelief occur by searching for an anime that contains the word "god" in a search engine?

It is not permissible to play games that contain what are claimed to be gods or anything that undermines Islamic belief, because it falls under the category of witnessing gatherings of disbelief. Allah has forbidden this, saying: "And He has already revealed to you in the Book that when you hear the verses of Allah being disbelieved in and ridiculed, do not sit with them until they engage in another conversation. Indeed, in that case, you would be like them."

Merely playing these games or researching their details is not disbelief if you detest and reject those acts of disbelief and do not consent to them. Merely uttering the names of gods carries no sin and does not expel one from the faith. It is advisable to turn away from obsessive thoughts and ignore them.