The Greek street food featuring meat cooked on a vertical rotisserie is gyros.
Gyros is made by stacking seasoned meat on a tall vertical spit that slowly rotates beside a heat source. As the outside cooks, the vendor slices off thin shavings, allowing the remaining meat to continue roasting. In Greece, pork is especially common, with chicken also widely served; lamb and beef appear in some versions and in restaurants outside Greece.
A typical gyros pita contains the sliced meat along with tomato, onion, fried potatoes, and tzatziki. The dish is usually wrapped in lightly grilled pita, although gyros meat can also be served on a plate. The vertical-spit technique developed in the Ottoman world, and Greek gyros is historically related to Turkish döner and Middle Eastern shawarma.
Those relatives are a frequent source of confusion, but the Greek name and usual Greek serving style make gyros the best answer here. Souvlaki generally means meat grilled on skewers, while kebab is a broad category of grilled or roasted meat dishes. Shawarma is the Middle Eastern counterpart rather than the canonical Greek term.