All big websites don't save pictures to the database they store them in the disk.
They save a reference to the picture's position in a table. And then link from there.
Why? Performance.
Pulling heavy content from a database is a huge performance bottleneck. And databases don't scale horizontally that well, so it would mean even a bigger problem. All big sites use static content farms to deal with static content such as images. That's servers who won't care less about your identity.
How do they keep the pictures really private you might ask? They don't.
The picture's link is, in itself, the address and the password. Let's take Facebook, for example. If I store a private picture on my account you should not be able to open it. But, as long as you have the correct address you can.
This picture is private. Notice the filename
10400121_87110566301_7482172_n.jpg
(facebook changes the url from time to time so the link may be broken)
It's non sequential. The only way to get the picture is to know it's address.
Based on a previous user photo you can't guess the next one.
It has a huge entropy so even if you start taking random wild guesses you'll have an extensive amount of failures and, if you do get to a picture, you won't be able to, from there, realize the owners identity which, in itself, is protection in anonymity.
Edit (why you should not store images in a "username" folder:
After your edit it became clear that you do intent to put files on disk and not on the database. This edit covers the new scenario.
Even though your logic (create a folder per user) seams more organized it creates problems when you start having many users and many pictures. Imagine that your servers have 1T disk space. And lets also imagine that 1T is more or less accurate with the load the server can handle.
Now you have 11 users, assume they start uploading at the same time and each will upload more than 100GB of files. When they reach 91GB each the server is full and you must start storing images on a different server. If that user/folder structure is followed you would have to select one of the users and migrate all of his data to a different server. Also, it makes a hard-limit on a user who can't upload more than 1T in files.
Should I store all files in the same folder, then?
No, big-sites generally store files in sequential folders (/000001/, /000002/, etc) having an x defined number of files per folder. This is mainly for file-system performance issues.
More on how many files in a directory is too many?