What should I do if two libraries provide a function with the same name generating a conflict?

It is possible to rename symbols in an object file using objcopy --redefine-sym old=new file (see man objcopy).

Then just call the functions using their new names and link with the new object file.

• If you control one or both: edit one to change the name and recompile Or equivalently see Ben and unknown's answers which will work without access to the source code.
• If you don't control either of them you can wrap one of them up. That is compile another (statically linked!) library that does nothing except re-export all the symbols of the original except the offending one, which is reached through a wrapper with an alternate name. What a hassle.
• Added later: Since qeek says he's talking about dynamic libraries, the solutions suggested by Ferruccio and mouviciel are probably best. (I seem to live in long ago days when static linkage was the default. It colors my thinking.)

Apropos the comments: By "export" I mean to make visible to modules linking to the library---equivalent to the extern keyword at file scope. How this is controlled is OS and linker dependent. And it is something I always have to look up.