You would want to first make sure that you have the correct filename and then proceed to the next step. The code should be: (assuming arcpy.Exists(buff_name)
does what it is supposed to do, because I think it should be arcpy.Exists(buff_name+str(100))
or something like it.)
import arcpy
arcpy.env.overwriteOutput = 1
arcpy.env.workspace="C:\\salzburg.gdb"
sbgRivers="sbg_rivers"
buff_name=raw_input("Please insert a new data set name:")
while arcpy.Exists(buff_name):
buff_name=raw_input("Name already exists. Please enter a new data set name")
for buffer_size in [100,200,300,450]:
arcpy.Buffer_analysis(sbgRivers,buff_name+str(buffer_size),buffer_size)
print "Buffer complete"
Your previous code would have run the for loop for all the inputs provided (even the wrong ones).