Customizing QgsProcessing output layer name

I’M writing an own QgsProcessing Algorithm and I want to give the output layer in the registry a custom name instead of the default "Output layer". I want to do that during processAlgorithm(), because I’d like to name the output after an input layer, adding a fixed name prefix.

I tried the setOutputLayerName() from the class QgsProcessingContext::LayerDetails, but it doesn’t change the name of the output. The example below is the "template" that the QGIS processing toolbox suggests for algorithm writing. Note the last third last and second last rows of the code, where I tried out my approach.

from qgis.PyQt.QtCore import QCoreApplication
from qgis.core import (QgsProcessing,
                       QgsVectorLayer,
                       QgsFeatureSink,
                       QgsProcessingException,
                       QgsProcessingAlgorithm,
                       QgsProcessingParameterFeatureSource,
                       QgsProcessingParameterFeatureSink)
from qgis import processing


class ExampleProcessingAlgorithm(QgsProcessingAlgorithm):
  
    INPUT = 'INPUT'
    OUTPUT = 'OUTPUT'

    def tr(self, string):
        return QCoreApplication.translate('Processing', string)

    def createInstance(self):
        return ExampleProcessingAlgorithm()

    def name(self):
        return 'myscript'

    def displayName(self):
        return self.tr('My Script')

    def group(self):
        return self.tr('Example scripts')

    def groupId(self):
        return 'examplescripts'

    def shortHelpString(self):
        return self.tr("Example algorithm short description")

    def initAlgorithm(self, config=None):
        self.addParameter(
            QgsProcessingParameterFeatureSource(
                self.INPUT,
                self.tr('Input layer'),
                [QgsProcessing.TypeVectorAnyGeometry]
            )
        )

        self.addParameter(
            QgsProcessingParameterFeatureSink(
                self.OUTPUT,
                self.tr('Output layer')
            )
        )

    def processAlgorithm(self, parameters, context, feedback):
        source = self.parameterAsSource(
            parameters,
            self.INPUT,
            context
        )

        
        if source is None:
            raise QgsProcessingException(self.invalidSourceError(parameters, self.INPUT))

        (sink, dest_id) = self.parameterAsSink(
            parameters,
            self.OUTPUT,
            context,
            source.fields(),
            source.wkbType(),
            source.sourceCrs()
        )

        # Send some information to the user
        feedback.pushInfo('CRS is {}'.format(source.sourceCrs().authid()))

        if sink is None:
            raise QgsProcessingException(self.invalidSinkError(parameters, self.OUTPUT))

        
        total = 100.0 / source.featureCount() if source.featureCount() else 0
        features = source.getFeatures()

        for current, feature in enumerate(features):
            # Stop the algorithm if cancel button has been clicked
            if feedback.isCanceled():
                break

            # Add a feature in the sink
            sink.addFeature(feature, QgsFeatureSink.FastInsert)

            # Update the progress bar
            feedback.setProgress(int(current * total))

        if False:
            buffered_layer = processing.run("native:buffer", {
                'INPUT': dest_id,
                'DISTANCE': 1.5,
                'SEGMENTS': 5,
                'END_CAP_STYLE': 0,
                'JOIN_STYLE': 0,
                'MITER_LIMIT': 2,
                'DISSOLVE': False,
                'OUTPUT': 'memory:'
            }, context=context, feedback=feedback)['OUTPUT']

        layer = QgsVectorLayer(baseName="My Output") # Create an empty layer for output naming
        context.layerToLoadOnCompletionDetails(dest_id).setOutputLayerName(layer) # Add this name to the output context
        return {self.OUTPUT: dest_id}

self.addParameter(
    QgsProcessingParameterFeatureSink(
        self.OUTPUT,
        self.tr('My output')
    )
)