Cooper and Smith are two surnames common among Romany people, formerly known as "Gypsies." Other names common in this group are not always derived from professions.
20000-names.com lists many other Romany/Gypsy surnames, including Petulengro, which is thought to come from the Romany term for a farrier, or horseshoe-maker; Boswell, a name derived from an old term for a settler; Grey, taken from the Sanskrit word for "horse"; Hearne/Herne, a name taken from heron and other types of birds; Lee; Lovel; Marshall; and Stanley.
FamilySearch.org confirms the above list of surnames and adds Young, Taylor, Draper, Shaw/Shore and Cooper. It also notes that Doe, Giaskin and Lock are common among Romany families.