There have been several suggestions to the significance of the name Stetson. Stetson was the name of a co-worker at the bank at which Eliot worked. However, Eliot's friends saw this as a reference to Eliot's American friend, Ezra Pound. The name may stand for "everyman"; a less common verson of Smith or Jones.
In 1988 Donald J. Childs proposed a more elaborate and complete an explanation. To him Eliot used the name Stetson to represent a soldier of the Australia and New Zealand Army Corp (ANZAC) and, in turn, the ANZACs signified the failed Gallipoli campaign of World War I. This was where Eliot's friend Jean Verdenal was killed. The ANZAC soldiers wore Stetson hats.
Childs' explanation of the use of Stetson connects him with parts of the poem in ways that the other explanations don't. Perhaps most obvious is the war connection between Gallipoli and the Punic War battle of Mylae mentioned on line 70. There would be plenty of corpses for Stetson to bury. There is also the connection with the brothel madame, Mrs. Porter (see the commentary attached to Eliot's note to line 199 ). Further, the rats that formed part of the life of the soldiers in the trenches appear here and there in The Waste Land.
The parade of the workers across the bridge line 62. may have reminded Eliot of the parades of the ANZAC veterans that several times marched through London.
In the same essay, Childs discussed the significance of the Smyrna merchant (see the Smyrna merchant commentary ).
Childs, Donald J., "Stetson in The Waste Land," Essays in Criticism, (April 1988) pp. 131-148