Basically, subroutine names are global. Perl does not have locally nested subroutines.

One possible way around it is to localize your changes to the symbol table:

local *evalsub;
eval $code;
evalsub();
[download]

Another way is to avoid using named subroutines and use code references:

my $code = 'sub { print "evalsub" }';

my $coderef = eval $code;

# Call our code
$coderef->();
[download]