As the name suggests, this type of soup pasta refers to the atmospheric phenomenon that sometimes devastates crops (grandina means hail in English). For this reason, we also find this pasta with the name tempestina (tempesta means storm in English). In Tuscany, this shape is often called grandinina:
“La grandinina. L’è… de’ pallini, piccini piccini… La prima pastina che si dà a’ bambini” (In Tuscan dialect, “Grandinina. It is … tiny tiny balls. The first pasta that you feed children”): T. Poggi Salani, N. Binazzi et al., Vocabolario del Fiorentino Contemporaneo, Accademia della Crusca (Contemporary Florentine Dictionary: Crusca Academy): http://www.accademiadellacrusca.it/it/scaffali-digitali/vocabolario-fiorentino).
The word soda (meaning firm in English) is added to grandine because it is “senz’i’ buco, tutta piena” (without a hole, all full) and the relative hardness of the dough increases the cooking time compared to its hollow version.
This shape is especially good in recipes with vegetable, fish or meat broth. In Livorno, grandina soda (called grandinina there) is traditionally prepared with shelled peas, fresh onions and meat broth.