In Opera 23 there are three ways to bookmark a website:
by adding the website to Speed Dial (a.k.a. Start Page), which supports folders.
by adding the website to Stash.
by adding the website to the Bookmarks Bar. In the bookmarks bar, you can create folders and folders within folders, as you wish. You can also right click (secondary click) to edit any entry and choose its name.
However, if this is not enough for you, Opera 25 introduces a new Speed Dial and bookmark manager. It's currently in alpha state, but it should be stable within the next few months.
Meanwhile, if there's anything we, the community, can do to help improving your browsing experience with Opera 23, feel free to ask.
Regards