In context: “Bramble” comes from Germanic bram-bezi, whence come also German Brombeere, Dutch Braambes and French framboise. It originated before the year 1000; Middle English; Old English bræmbel, variant of brǣmel, equivalent to brǣm– (cognate with Dutch braam broom ).
Bramble bushes have long, thorny, arching shoots and root easily. They send up long, arching canes that do not flower or set fruit until the second year of growth. Brambles usually have trifoliate or palmately-compound leaves.
Bramble fruits are aggregate fruits. Each small unit is called a drupelet. In some, such as the blackberry, the flower receptacle is elongated and part of the ripe fruit, making the blackberry an aggregate-accessory fruit.
You can choose to see the name as refering to the cakes’ bushy look or refering to the fact that they contain blackberry jelly – Ted