I think you will need to use a custom script which checks the name of the input layer. If the script allows that name then the rest of the model can be executed otherwise it will produce an error message.
You can create a script from:
Processing Toolbox > Scripts > Tools > Create new script
Then use something like the following:
##Example=name
##input_layer=vector
##output=output vector
from qgis.utils import iface
from qgis.gui import QgsMessageBar
layer = processing.getObject(input_layer)
# Add your names into the list within single quotes
allowed_layers = ['map', 'layerName2', 'layerName3']
if layer.name() in allowed_layers:
output=input_layer
else:
iface.messageBar().pushWidget(iface.messageBar().createMessage( u'Layer not allowed' ), QgsMessageBar.WARNING, 3)
Make sure the script is saved in your /.qgis2/processing/scripts/ directory. Then in your modeler, include the script immediately after your vector input and set its input parameter to be from the vector input. Add the first function to take the output from the script as its input.
For example:

Now when you run your model, if the selected layer is not mentioned in the script, it will fail to run:

Save selected featurestool after the script :) – Joseph Jun 12 '17 at 10:00ifstatement in the script :) – Joseph Jun 13 '17 at 09:37