A quick look-up in *A Dictionary of Surnames* (Hanks & Hodges) finds the name "Talmadge" under the entry for "Tollemache". The definition given is:
Tollemache: English : apparently a metonymic occupational name for an itinerant merchant, from Old French "talemasche" knapsack (of uncertain origin.
Variations: Tallemach, Tallamach, Talma(d)ge, Tammage. (The form "Talmadge" has also been used as an Anglicized form of one or more like-sounding Jewish surnames.)