Changing your code to this will avoid the name collision problem - rename will overwrite a duplicate named file.

#!/usr/bin/perl
$dir = "./test";
opendir(DIR,$dir) || die "NO SUCH Directory: $dir\n$!";

foreach $zips (readdir DIR){
    $new_name = $zips;
    $new_name =~ s/\.log/\.txt/ig;
    rename ("$dir/$zips","$dir/$new_name") unless ($zips eq $new_name)
+;
}
close(DIR);
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jdtoronto