You can #include arbitrary files in a C++ translation unit (the *.cpp you are compiling) provided the preprocessed form (after pre-processing) is valid C++. Read some documentation on the preprocessor and the C preprocessor wikipage. Don't forget that preprocessing is the first phase in a C or C++ compiler. (Historically, it was even a different process /lib/cpp; now it is inside the compiler for performance reasons).
The name of the included file does not matter much. Conventionally, you don't want to name an included file to look like a top-level translation unit. This is why people generally do not #include "example.cpp" but something like e.g. #include "example.inc" or #include "example-inc.cpp" (or #include "example.def", specially if you #include several times a header). The standard C++ library accepts #include <map> for example.
See for example this answer which shows some included file which is #include-d several times (for different purposes), or, inside the GCC source tree, the file gcc/tree.def
Of course, you cannot #include several times an arbitrary C++ file in the same compilation unit (because you cannot have several definitions of e.g. the same function).
In practice, use e.g. g++ -C -E foo.cc > foo.ii to get the pre-processed form of translation unit foo.cc ... then look with a pager or editor into the preprocessed form foo.ii
Read also about some proposal on modules in C++. It was not accepted in the latest C++ standard, but something similar might perhaps become standardized in the future.
example.hppanywhere else besides yourmain.cppif you include the corresponding source there. Stop that nonsense please! Immediately!