Contrary to the implication of the question, there is no single named forest covering the Yucatán Peninsula. Instead, the region is a mosaic of low and medium tropical deciduous and semi-evergreen forests, interspersed with scrubland (matorral), savanna, wetlands, and coastal mangroves.
The Yucatán's forests form part of the Mesoamerican Biological Corridor, harboring jaguars, tapirs, howler monkeys, and hundreds of bird species. Major protected areas include the Calakmul Biosphere Reserve (Mexico), Río Bravo Conservation Area (Belize), and Maya Biosphere Reserve (Guatemala).
So while no single "forest" bears the peninsula's name, its collective forest cover is ecologically vital and globally significant.