There are many different instances of the "fragment" or "ruins" motif in this poem that appear through different mediums. Sometimes Eliot uses the formatting of the poem to create fragments, which can be seen in "II. A GAME OF CHESS" by the fragmented language. Other times, as he does in this stanza, he personifies fragmentation. This paragraph signifies the motif of fragmentation by fragmenting a character in the story into two separate people. One way of viewing these lines is that the person the narrator is describing is leading a double life or double consciousness, and the narrator is now seeing this person's doubleness. Another interpretation- that seems to be the most popular- is that the narrator is hallucinating that there is another person walking with them.
This interpretation comes from the story of Ernest Shackleton, a polar explorer that lead expeditions to Antarctica, who cited in one of his books that he once hallucinated while on an expedition. This explanation covers why the narrator is looking "ahead up the white road". "The Wasteland" was written shortly after WWI ended, leaving some of the world in ruins and fragmented apart from each other. Eliot could be citing Shackleton's hallucination experience because the world (especially the US) was experiencing its own post-war hallucinations of grandeur during the party age of the 1920s. Much of the 1920s was about forgetting the troubles of the world and pretending like life was fine and dandy. The people of this time not only created their own hallucinations of a better life, but created a double consciousness for themselves by buying into these hallucinations. Fragmentation can also be a form of compartmentalization, which is exactly what the time period that the poem was written in, was about.