I did exactly same as install instruction, and :scriptnames doesn't show surround plugin. surround command doesn't work at all. Used vim8 package manager.
I followed this instruction:
mkdir -p ~/.vim/pack/tpope/start
cd ~/.vim/pack/tpope/start
git clone https://tpope.io/vim/surround.git
vim -u NONE -c "helptags surround/doc" -c q
Not sure why it doesn't work, but you might consider using one of the plugin managers for all your plugins. Even though it's not explicitly stated, but you can always use a plugin manager like Vim-Plug, Vundle, Pathogen etc. to install most plugins (git is required). The website vimawesome.com includes the major plugins, their README.md, and their installation methods for different plugin managers. Here's the link for surround.vim on vimawesome: https://vimawesome.com/plugin/surround-vim
Personally I used Vim-Plug to install surround.vim without any problem. Hope you like it!