how can i add an element of argv to a variable and print it?

my $name = shift @ARGV; does indeed assign the program’s first argument. If you get Use of uninitialised value $name in concatenation (.) or string at ..., it’s because you didn’t provide any arguments to your program.

$ perl -we'my $name = shift(@ARGV); print "My name is $name.\n"'
Use of uninitialized value $name in concatenation (.) or string at -e line 1.
My name is .

$ perl -we'my $name = shift(@ARGV); print "My name is $name.\n"' ikegami
My name is ikegami.

There’s absolutely no problem with using <> afterwards.

$ cat foo
foo1
foo2

$ cat bar
bar1
bar2

$ perl -we'
   print "(\@ARGV is now @ARGV)\n";
   my $prefix = shift(@ARGV);

   print "(\@ARGV is now @ARGV)\n";
   while (<>) {
      print "$prefix$_";
      print "(\@ARGV is now @ARGV)\n";
   }
' '>>>' foo bar
(@ARGV is now >>> foo bar)
(@ARGV is now foo bar)
>>>foo1
(@ARGV is now bar)
>>>foo2
(@ARGV is now bar)
>>>bar1
(@ARGV is now )
>>>bar2
(@ARGV is now )