Bola de gude (often bolinha de gude) is the nationwide umbrella term, but ALiB's question 156 reveals strong regional layers. Peteca dominates the Amazonian dialect area; bila is a major Northeastern answer; and the South has bolita, búrica and biloca alongside bola de gude. Minas records a cluster of birosca/biloca/bilosca, while the Fluminense area records boleba.
These are survey frequencies, not borders. Children can know several names, and the ordinary meaning of peteca is still the hand-struck shuttlecock. The map paints the strongest documented association first and shows lower-frequency forms as “also used.”