Insert the name of file inside the file

Question

I have in a directory some *.csv files. I want to insert inside each file, its name.

The following code do it, but I also need to remove, delete the pattern .csv

for file in *.csv; do echo "$file,"$"$(cat -- "$file")" > "$file"; done

for example if the name is London.csv and inside I have 10, 20, now I get

London.csv, 10, 20

I need to reduce it to,

London, 10, 20

With your help, I get it with this update

for file in *.csv; do echo ${file%.csv},"$"$(cat -- "$file")" > "$file"; done