Pre-ME1: Only known to military. Respected and trusted in it.
ME1: As first human Spectre, gains wide (if temporary) coverage and respect. He is known to the Citadel and human audiences. He is still 'on same the level' when speaking to people, but still carried or brought up an authority (whether given by the Council or asserted as a soldier).
ME2: Defeating Sovereign and Saren brought (the original) Shepard to a combined reputation as a top N7, first human Spectre, and savior of the Citadel. After his death, he is memorialized and used in media, including recruitment propaganda for the Alliance. However, due to the circumstances of Shepard's journey and politics, it was easy to decide to cut short the attention on him. Nonetheless, his story of saving the Citadel becomes a legend of sorts, and known throughout the galaxy, in good and bad ways. After returning, Shepard is known to be exploring and visiting much of the galaxy, but the nature of his resurrection and his Cerberus ties, as well as frequent discrediting, has him shrouded. He is probably spoken of, but in very nebulous terms. Anything about his fight against the Collectors is not widely known, at least not until the Reaper War. Shepard exists as a walking symbol, but in the shadow, not yet in the light.
ME3: Shepard is made known to the galaxy yet again, as a major part of the war effort. He is a man fighting on the ground with armies, a symbol inspiring the wider galaxy, and a savior to the fate of the whole galaxy. He is drawn out of the shadow and a bit into the light. While Shepard had a reputation in ME1 that became an appeal in ME2, he becomes perhaps the most famous person in the galaxy in ME3, even if there can be degrees of mandatory or optional infamy. Shepard can more actively work to credit... or discredit himself as good or bad in everyone's eyes, but regardless, he's someone who gets things done and is ensuring the safety of the galaxy during a time of extinction. Shepard realizes by now how much people look up to him (though lines in ME3 focus on this just to let new players realize it), and acts accordingly as someone who either lifts the galaxy up, or pushes them to lift themselves up, or go beyond all that and change the whole nature of the galaxy (Krogan cure peace, Rannoch peace, Synthesis).
Throughout all of this, Shepard is a controversial figure, who on one hand is trusted and regarded as a capable hero of the galaxy, and on the other is seen as a human upstart with immoral connections. He's a renegade. He's a paragon. He might be the savior. He might be our doom.
Shepard is a legend in some quarters even pre-ME1 with his service history, but ME1 secures him in the galaxy as important, then the ME2+ME3 secures him as the MOST important. This comes with making enemies, but it also came with eventually massive popularity (whether Shepard more shrugs it off or accepts it). In ME1 it is the rare person knowing who you are, but in ME2 its more like the occasional fan who would do things for you, but in ME3 it is technically whole armies fighting Reapers in the vocal name of Shepard.
Throughout it all, Shepard can be seen as, and we can even RP Shepard as a naive, overly trusting, betraying, psychopathic, sociopathic, person. Sort of. He never goes the full way there, but only has more and more of those cracks show, yet with the countering of more forced scenes showing a humanity. So he can have bad reputations, and we can see why that might be, but ultimately we side with him and his struggle, acknowledging that he has some bad press and gossip.
One element is that Shepard is viewed by many as kinda nutty. In ME1 this was about his warnings about the Reapers. In ME2 this was about his dealings with Cerberus (and optionally the Arrival incident). In ME3 it is the insistence on the Crucible plan. All of these go against normally logical plans for people, but we as the player see how they could make more sense than the alternative. In any case, this makes Shepard a sort of 'Renegade' in all games, to some degree, in his interactions with the galaxy throughout the trilogy. He isn't automatically trusted, but he has to work for it (finally symbolized by the 'Reputation' bar in ME3). He's a great soldier because he trained, he's a great symbol because he was successful, and he's a great savior because he put himself in the right place at the right time. There's very little (at least so far) to communicate a story of Shepard's life being preordained, and even Leviathan calls him an 'anomaly'. For the story we have in the trilogy, we have a man who, sure, lucked out, but the biggest explanation of his successes, victories, and accomplishments is that he was simply a person who decided to act and act well.