I don't think that construct has a specific name - it's just using parentheses to change precedence. Usage examples for s/// can be found in Regexp Quote-Like Operators; examples for y/// (although its synonym tr/// is used in these examples) can be found in Quote-Like Operators.
In Perl 5.14.0, an r option was introduced (see perl5140delta under Core Enhancements - Regular Expressions - Non-destructive substitution). This makes the following equivalences:
# For y///
(my $x = $y) =~ y///;
my $x = $y =~ y///r;
# Ditto for its synonym tr/// (although not mentioned in perl5140delta
(my $x = $y) =~ tr///;
my $x = $y =~ tr///r;
# And for s///
(my $x = $y) =~ s///;
my $x = $y =~ s///r;
The first two links above are for the current Perl version (5.16.0 at the time of writing) so they have examples of this also.