Saving shapefile layer as KML with datasourceOptions using PyQGIS

datasourceOptions are passed as a list of OGR creation options for the format.

There are 2 ways: writeAsVectorFormatV2() and writeAsVectorFormat().

The first one is more neat in my opinion:

options = QgsVectorFileWriter.SaveVectorOptions()
options.driverName = "KML"
options.fileEncoding = 'utf-8'
options.datasourceOptions = ["NameField=ulica"]

QgsVectorFileWriter.writeAsVectorFormatV2(layer=inputLayer, fileName=fileName, transformContext=QgsCoordinateTransformContext(), options=options)

Second option:

QgsVectorFileWriter.writeAsVectorFormat(layer=inputLayer,
                                            fileName=fileName,
                                            fileEncoding='utf-8',
                                            destCRS=crs,
                                            driverName="KML",
                                            datasourceOptions=["NameField=ulica"]
                                            )

PS. How I found the answer to your question:

Here is the documentation of QgsVectorFileWriter. The datasourceOptions parameter is described as a list of OGR data source creation options.

Here I looked up KML format Creation options in the GDAL/OGR documentation. Every format has its own specific creation options. If you need to specify any other options you just pass them in the list just as you would pass them if you used OGR/GDAL in command line.