Are you sure you are having the file "name" and/or "/home/name" ?
better remove the -s option just for testing so-that you can see what is going wrong there.
Just guessing, but it looks like you're trying to determine if $1 is a full (absolute) path (and if so, echo "Wrong, full path"), or a relative path (and if so, echo 1 according to your code?)
try this:
while [[ $# -gt 0 ]]; do
fullPath=$(echo $1 | grep -sc '^/')
echo $fullPath
if [[ $fullPath -gt 0 ]]; then
echo "Wrong, full path"
fi
shift
done