> With luck, make considers first "Makefile" name and then "makefile", 
> but adding a little check should not be a big challenge.
GNU make considers GNUmakefile, makefile then Makefile
Makefile is more usual than makefile (and is recommended in the man page...)

> The name is determined by the "make" command, since it is called to build
> the project.
The -f switch for make allows another filename to be specified - although
I've not (yet) looked at the plugin this would probably be useful for
projects that have Makefile (for UNIX) and Makefile.nt (for Windows)