JSFiddle - React, Tailwind, and code Playground

HTML

<form name="campos" method="post" action="<?=$PHP_SELF?>">
    <label> <span>Nome:</span>

        <input type="text" name="nome" placeholder="" />
        <br/>
    </label>
    <label> <span>Cargo:</span>

        <input type="text" name="cargo" placeholder="" />
        <br>
    </label>
    <label> <span>Celular:</span>

        <input type="text" name="celular" placeholder="Exemplo: 44 9876 9876" />
        <br/>
    </label>
    <label> <span>e-mail:</span>

        <input type="text" name="email" placeholder="" />
        <br>
    </label>
    <input type="hidden" name="acao" value="enviar" />
    <button type="submit" class="envio" title="Enviar mensagem"></button>
</form>

JavaScript

$(window).load(function () {
    $("input[name=nome]").change(function () {
        var partes = this.value.split(' ');
        var email = partes[0];    
        $("input[name=email]").val(email.toLowerCase() + "@dominio.com.br");
    });
});