If the output format (extension) is different from the input format, the files won't get overwritten. If they are the same, you can use this trick, that makes them appear to be "different" for this purpose but are really the same but differ in the case of the extension:
gm mogrify -resize 150x150 -format PNG +profile "*" *.png
EDIT:
I don't know of a facility within "mogrify" to rename the output files other than specifying a different directory or a different extension. So fragphace's answer is correct; you will need to use a script to rename them. In combination with my answer:
gm mogrify -resize 150x150 -format PNG +profile "*" *.png
for file in *.PNG
do
basename=`echo $file | sed -e "s/.PNG//"`
mv $basename.PNG $basename-thumbnail.png
done