use v5.10;

my $str = 'variable_name, VARIABLE_NAME, _var_x_short,  __variable__name___';

### solution 1
$_ = $str;

$_ = lc;
s/_(\w)/\U$1/g;

say;

### solution 2: multi/leading underscore fix
$_ = $str;

$_ = lc;
s/(?<=[^\W_])_+([^\W_])|_+/\U$1/g;

say;

### solution 3: without prior lc
$_ = $str;

s/(?<=[^\W_])_+([^\W_])|([^\W_]+)|_+/\U$1\L$2/g;

say;