The short answer is that he wasn't very "famous" in his time (i.e. release an album and make a name for yourself, like Bob Dylan), and neither was he "famous" for around two decades until after his death. His fame reached only to his circle of friends (some famous blues musicians themselves), those involved in his performance life, and those who chose to pay attention to him, which I go into more in depth below.
For the most part, he was known around a couple of states as a itinerant musician, but it's a little more complicated than that.
Now well on his way to becoming a polished professional, Johnson established a base in Helena, Arkansas, and worked extensively throughout the South as a walking musician, traveling sometimes alone and sometimes with other guitar players, such as Johnny Shines or Calvin Frazier. He frequently traveled and played under assumed names, a habit that complicated later efforts to construct an accurate biography. It was during this time, between his late teens and midtwenties, that Johnson began to absorb, blend, and refine particular stylistic nuances—drawn from piano as well as guitar—that would eventually help redefine blues for a new generation of musicians who left the South and moved to St. Louis, Detroit, and most prominently, Chicago.
Although Johnson was well known in Arkansas, Mississippi, and Tennessee by the midthirties, he yearned to record, as many of his mentors and influences already had. So, according to most accounts, he traveled to Jackson, Mississippi, to audition for H. C. Speir, a music-store owner whose ear for talent had led to recording sessions for a veritable who's who of important regional blues artists during the twenties and thirties.
Barry Lee Pearson, Billy McCulloch, "Robert Johnson: Lost and Found." University of Illinois Press, 2003
More interesting is Bob Dylan's account of coming to know of Robert Johnson's music, from Dylan's Chronicles: Volume One, which says a lot about how his fame came to elevate in the years after his death.
Before leaving that day, [John Hammond, a record producer for Columbia Records had] given me a couple of records that were not yet available to the public that he thought might interest me. Columbia had bought the vaults of ’30s and ’40s secondary labels — Brunswick, Okeh, Vocalion, ARC — and would be releasing some of the stuff.
One of the records that [John Hammond] gave me was The Delmore Brothers with Wayne Rainey, and the other record was called King of the Delta Blues by a singer named Robert Johnson. Wayne Rainey, I used to hear on the radio and he was one of my favorite harmonica players and singers, and I loved The Delmore Brothers, too. But I’d never heard of Robert Johnson, never heard the name, never seen it on any of the compilation blues records. Hammond said I should listen to it, that this guy could "whip anybody." He showed me the artwork, an unusual painting where the painter with the eye stares down from the ceiling into the room and sees this fiercely intense singer and guitar player, looks no more than medium height but with shoulders like an acrobat. What an electrifying cover. I stared at the illustration. Whoever the singer was in the picture, he already had me possessed. Hammond told me that he knew of him from way back, had tried to get him up to New York to perform at the famous Spirituals to Swing Concert but by that time he had discovered that Johnson was gone, had died mysteriously in Mississippi.
I had the thick acetate of the Robert Johnson record in my hands and I asked [Dave] Van Ronk if he ever heard of him. [...] Dave thought Johnson was okay, that the guy was powerful but that it was all derivative. [...] The record that didn’t grab Dave very much had left me numb, like I’d been hit by a tranquilizer bullet.
Johnson recorded in the '30s, and in the 1960s there were still some folks around in the Delta who had known about him. Some even, who knew him. There’d been a fast moving story going around that he had sold his soul to the devil at a four-way crossroads at midnight and that’s how he got to be so good. Well, I don’t know about that. The ones who knew him told a different tale and that was that he had hung around some older blues players in rural parts of Mississippi, played harmonica, was rejected as a bothersome kid, that he went off and learned how to play guitar from a farmhand named Ike Zinnerman, a mysterious character not in any of the history books. Maybe because he didn’t make records.
You gain some insight about Robert Johnson's living years, and the decades after his death from reading Bob Dylan's accounts, and his connection with John Hammond and Dave Van Ronk, who either knew Johnson personally, or knew of him and his work. It's also worth noting that Dave Van Ronk was roommates with Sam B. Charters (a music historian), who wrote The Country Blues, which detailed a chapter on Robert Johnson, a crazy connection between all these people! More importantly, you gain an insight of just how influential Johnson's limited recordings are (even on Bob Dylan himself, read more about it in his autobiography) and how his recordings seeped from one era to the next, from one musician or producer to the next musician or producer.