I want to split the URL at the first '/' or first '#' and use it.

Then maybe just try

for my $url ("www.abcd.com?file/search",
             "www.abcd.com/search",
             "www.efgh.in#found") {

    my ($fname) = split /[\/#]/, $url;
    
    print $fname;
}

__END__
www.abcd.com?file
www.abcd.com
www.efgh.in
[download]

split takes a regular expression by which to split the string, and [\/#] is a character class comprising the two characters '/' and '#', which means to split on either of those characters.  The parentheses around $fname in the assignment are needed to supply list context for split.