package ECHO_MODULE;

sub say_hi {print "hi\n";}
sub say_bye {print "bye\n"}

package main;
print "enter subroutine name: ";
chop ($subname = <STDIN>);

if (ECHO_MODULE->can($subname) ) {
    ECHO_MODULE->$subname();
} else {
    print "sub '$subname' not defined.\n";
}
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Read the perl documentation, namely perlrun, perlsub, perlref... anything, all, more.

update, as per privmsg from memnoch:

For the can() method, see perlobj: it resides in the module UNIVERSAL from which all classes implicitly inherit as their last base class. As chromatic pointed out below, the method can() returns a subroutine reference for its argument, and calling a sub as method or function makes a difference. ECHO_MODULE->$subname() will get ECHO_MODULE as its first argument, while ECHO_MODULE->can($subname)->() will not. It all depends on the design of the package - is it a functional package (a.k.a library) or a class?

_($_=" "x(1<<5)."?\n".q·/)Oo.  G°\        /
                              /\_¯/(q    /
----------------------------  \__(m.====·.(_("always off the crowd"))."·
");sub _{s./.($e="'Itrs `mnsgdq Gdbj O`qkdq")=~y/"-y/#-z/;$e.e && print}