If you're worried about the total size of the if {} else {} clause, you could give the ternary conditional operator (?:) a try (assuming your code doesn't continue below the ternary operator statement in this peculiar case):

($name eq "")
  ? print q{Sorry, name can't be empty}
  : print "Thank you, $name. Your submission is complete.";
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(Sorry to reply so late but) this looks very wrong to me: the ternary operator is designed to operate on values, not to use it as a general purpose branching tool for its side effects. I would never do so except in golf: in particular the above example becomes perfectly fine if you amend it by factoring out the print:

print +($name eq "")
  ? q{Sorry, name can't be empty}
  : "Thank you, $name. Your submission is complete.";
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