If you want a little bit of invisibility, you might seek anonymity, or being anonymous and nameless. He was a very wealthy man, and he gave most of his money away with quiet anonymity, so no one knew who was helping.
The noun anonymity comes from a Greek word meaning "without a name." If you have anonymity, you have namelessness, and people will not know who you are. Some words that are the opposite of anonymity are "celebrity" and "fame." Sometimes people request anonymity, as in "he phoned the police to report the break-in across the street but requested anonymity so the burglars wouldn't know who turned them in."