The way to specify the name of the makefile is with the `-f' or `--file' option (`--makefile' also works). For example, `-f altmake' says to use the file altmake as the makefile.
If you use the `-f' flag several times and follow each `-f' with an argument, all the specified files are used jointly as makefiles.
If you do not use the `-f' or `--file' flag, the default is to try GNUmakefile, makefile, and Makefile, in that order, and use the first of these three which exists or can be made (see Writing Makefiles).