diff --git a/testutil/names.go b/testutil/names.go
index a3d2acd3c1..ee182ed50b 100644
--- a/testutil/names.go
+++ b/testutil/names.go
@@ -10,6 +10,8 @@ import (
 
 var n atomic.Int64
 
+const maxNameLen = 32
+
 // GetRandomName returns a random name using moby/pkg/namesgenerator.
 // namesgenerator.GetRandomName exposes a retry parameter that appends
 // a pseudo-random number between 1 and 10 to its return value.
@@ -19,5 +21,20 @@ var n atomic.Int64
 // to the return value.
 func GetRandomName(t testing.TB) string {
 	t.Helper()
-	return namesgenerator.GetRandomName(0) + strconv.FormatInt(n.Add(1), 10)
+	name := namesgenerator.GetRandomName(0)
+	return incSuffix(name, n.Add(1), maxNameLen)
+}
+
+func incSuffix(s string, num int64, maxLen int) string {
+	suffix := strconv.FormatInt(num, 10)
+	if len(s)+len(suffix) <= maxLen {
+		return s + suffix
+	}
+	stripLen := (len(s) + len(suffix)) - maxLen
+	stripIdx := len(s) - stripLen
+	if stripIdx < 0 {
+		return ""
+	}
+	s = s[:stripIdx]
+	return s + suffix
 }
diff --git a/testutil/names_internal_test.go b/testutil/names_internal_test.go
new file mode 100644
index 0000000000..7fabc0a8c3
--- /dev/null
+++ b/testutil/names_internal_test.go
@@ -0,0 +1,52 @@
+package testutil
+
+import (
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+func TestIncSuffix(t *testing.T) {
+	t.Parallel()
+
+	for _, tt := range []struct {
+		s      string
+		num    int64
+		maxLen int
+		want   string
+	}{
+		{
+			s:      "foo",
+			num:    1,
+			maxLen: 4,
+			want:   "foo1",
+		},
+		{
+			s:      "foo",
+			num:    42,
+			maxLen: 3,
+			want:   "f42",
+		},
+		{
+			s:      "foo",
+			num:    3,
+			maxLen: 2,
+			want:   "f3",
+		},
+		{
+			s:      "foo",
+			num:    4,
+			maxLen: 1,
+			want:   "4",
+		},
+		{
+			s:      "foo",
+			num:    0,
+			maxLen: 0,
+			want:   "",
+		},
+	} {
+		actual := incSuffix(tt.s, tt.num, tt.maxLen)
+		assert.Equal(t, tt.want, actual)
+	}
+}