Depends what you mean by "meaningless".
Obviously, moral discourse means a variety of things to a variety of people, though I suppose Wittgenstein would say it is meaningless, without advocating nihilism. So I suppose you mean normatively meaningless, rather than descriptively so.
If you mean 'false' then "error theory", which seems to have a rich live tradition.
If you mean 'illogical' then at least some forms of non-cognitivism, such as Ayer's subjectivism, would class.
If you believe that right and wrong, or perhaps value in general, merely has no bearing on practical affairs of the world, then you are a practical moral sceptic.
I don't know which philosophers define their contemporary approach with the word "moral nihilism", but there are many historical nihilists
Camus seems to think almost everyone is a "nihilist"
By an “inevitable logic of nihilism” Communism climaxes the modern
trend to deify man and to transform and unify the world. Today’s
revolutions yield to the blind impulse, originally described in The
Myth of Sisyphus, “to demand order in the midst of chaos, and unity in
the very heart of the ephemeral” (MS, 10). As does the rebel who
becomes a revolutionary who kills and then justifies murder as
According to Camus, the execution of King Louis XVI during the French
Revolution was the decisive step demonstrating the pursuit of justice
without regard to limits. It contradicted the original life-affirming,
self-affirming, and unifying purpose of revolt. This discussion
belongs to Camus’s “history of European pride,” which is prefaced by
certain ideas from the Greeks and certain aspects of early
Christianity, but begins in earnest with the advent of modernity.
Camus focuses on a variety of major figures, movements, and literary
works: the Marquis de Sade, romanticism, dandyism, The Brothers
Karamazov, Hegel, Marx, Nietzsche, surrealism, the Nazis, and above
all the Bolsheviks. Camus describes revolt as increasing its force
over time and turning into an ever more desperate nihilism,
overthrowing God and putting man in his place, wielding power more and
more brutally. Historical revolt, rooted in metaphysical revolt, leads
to revolutions seeking to eliminate absurdity by using murder as their
central tool to take total control over the world. Communism is the
contemporary expression of this Western sickness.
I mean you can see the tension there: if God is dead and we cannot put humanity in its place then how can we know our practical obligation etc..