$$file =~ 
s/<%[ ]*link_name[ ]*([^ ]*)[ ]*%>(?{push(@link_names,$1);})/<% link_name $1%>/g;

#can be rewritten as (changed single space to \s, might
# be more usefull

$$file =~ s{
   <% \s* link_name \s* (\S*) \s* %>
}{ push @link_names,$1; "<% link_name $1 %>" }xg;

# but in fact you don't even need s///

while($$file =~ 
  m{ <% \s* link_name \s* (\S*) \s* %> }xg
){
  push @link_names,$1
}