2 folders added to PATH contain different files with the same name

The directories listed in the PATH variable will be searched in the order in which they are listed. When the given command is found, the search ends.

This means that if you added the two directories in the order that you show (folder1 before folder2), then the command from folder1 will be used if you just say filewithname.sh on the command line. The folder1 variant of the command effectively shadows the variant in folder2.

If you want the other variant of command, you will have to access it using its path, i.e. as /home/example/folder2/filewithname.sh, or via some equivalent pathname.

You may also create aliases for each of the commands so that you don't have to think about what order the directories are listed in $PATH. For example,

alias c1=/home/example/folder1/filewithname.sh
alias c2=/home/example/folder2/filewithname.sh

This would allow you to use c1 and c2 to execute the two scripts.

You could put these alias definitions in your shell's initialization file (e.g. in ~/.bashrc if you're using bash, or in ${ZDOTDIR:-$HOME}/.zshrc if you're using zsh).