I set the legend text using the code below but upon saving, closing and reopening the QGIS project the legend text reverts back to the layer name.
project = QgsProject.instance()
manager = project.layoutManager()
layout = manager.printLayouts()[0]
legend = QgsLayoutItemLegend(layout)
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legend.setAutoUpdateModel(False)
root = legend.model().rootGroup()
root.removeAllChildren()
leg_layer = root.addLayer(layer)
leg_layer.setUseLayerName(False)
leg_layer.setName('layer legend text')
legend.model().setRootGroup(root)
layout.addLayoutItem(legend)