Both prefixed to and prefixed by are correct, but they have different meanings.
If A is prefixed to B, A is the prefix and B is what the prefix is added to. In this case the end result is A_B. To use your example, you could say that
user is prefixed to
load() to create
If A is prefixed by B, B is the prefix and A is what the prefix is added to. The result is B_A. For your example, you would say that
load() is prefixed by
user to create
To state this in more general terms for your entire project, you might make either of these statements:
Each method name related to the
user object is prefixed by the string
user is prefixed to each method name related to the
And concerning the sentence in your question:
Functions implemented by a module should always have their names prefixed by the module name.
It is indeed correct, because the suffix (function name) is prefixed by the prefix (module name).