Shared objects are not loaded when they are next to a particular file, but when their directory is in the library load path. The operating system sets a few paths that are valid for all programs, but if you have your library elsewhere, you need to specify the directory yourself.
Exporting LD_LIBRARY_PATH
with the dir of the library will let the library loader know what other paths you expect to load a library from. E.g. if you built libgit2 with the libgit2sharp script you might run
export LD_LIBRARY_PATH=$HOME/libgit2sharp/libgit2/build
in the console to let the OS know that any program you start from that shell where to find libgit2.
It's common for mono-based apps to provide a script for the user to run which sets up the environment before calling mono to start the actual .exe
with the program.