In your code you try to save a raster with name "Script_First_10_HH" which exceed allowed name length (13 characters) of GRID raster.The script which iterates through several shapefiles and for each crates new raster may look like that: import arcpy, sys, traceback, os
arcpy.CheckOutExtension("Spatial")
#set pathes
arcpy.env.workspace = r"C:\tmp\Shp"
outRasterDir = r"E:\VTA\TEST\output\Distance_from_Household\Script_First_10_HH"
#your variables
maxDistance = 100000
cellSize = 1000
shpList = arcpy.ListFeatureClasses("P*")
for shp in shpList:
#build the name of output raster: directory + shapefilename w/o extension + some text
outRaster = os.path.join(outRasterDir, shp[:-4] + "_EucD")
#run the tool (if you want use defaults instead of maxDistance and cellSize, place "" instead of variable name)
outEucDist = arcpy.sa.EucDistance(shp, maxDistance, cellSize)
outEucDist.save(outRaster)