Fame is not greatness and may be only self-promotion. Celebrity is not admirable in and of itself. The day Jesus died, He was less well loved than Barabbas.
What is required for real, inner greatness? I think we have to distinguish between inner greatness and hidden greatness. For instance, the aforementioned Jesus never vaunted Himself, preferring to point to the Father, but His own inner greatness could not possibly be hidden. If we can hide greatness within, is it greatness at all? Crowds followed Jesus. He often discouraged them from following Him. He more often pointed out the cost to following Him. At one point Jesus admonished His closest followers to know they could live well as long as they followed Him, then completely redefined what it means to live well.
His is inner greatness of the kind that could not be hidden.
The inner greatness of Jesus never involved how He dressed or how He got from place to place. In fact, there is no mention in Scripture of His externals. The kinds of things cultic Christians use to identify the level of our belief is not a part of Jesus' mission. He is great, inwardly, in ways no one seriously denies are the stuff of value: love, compassion, strength of character, consistency of mission, self-sacrifice, service, communal values.
The only mention of Jesus' personal habits concern His habits around common meals. He eats food gleaned on the Sabbath and He dines regularly with unsavory persons when He could occupy Himself with religious persons only. Each time, His detractors are religious persons who make no mention of His consistent mission. Instead, they decry His violations of their interpretive traditions.
They are fanatics, even if luke-warm. A fanatic is that fellow who insists there is Truth, he has it, you have to get it from him, the way he got it and hold it the way he holds it. A fanatic is every bit as destructive as a nihilist and usually more active.
Fanaticism is a spiritual issue of inner smallness. A fellow can be known the world around and still be small inside. He will eventually demonstrate his tiny inward person, if only in this: he never exhibits meaningful goodness.
A good tree bears good fruit.
A great tree bears good fruit more than one season.
Opinions expressed here are mine alone.