您似乎已经具备了从表的每一行中检索名称和月份的逻辑，因此要达到您的目标，您所需要做的就是对数组使用includes()方法，以确定当前的name是否存在于其中，并直接比较月份名称的字符串。
我建议在tr上进行此比较，而不是在td子级上，因为这样可以使hide()/show()的逻辑更加简单明了：

jQuery($ => {
  const names = ["Abe D", "Jon R"];
  const mth = "Feb"

  $("button").click(function() {
    $('tbody tr').hide().filter((i, tr) => {
      const $tr = $(tr);
      const name = $tr.children('td:nth-child(2)').text().trim();
      const month = $tr.children('td:nth-child(3)').text().trim();
      return names.includes(name) && month === mth;
    }).show();
  });
});

<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<table>
  <thead>
    <tr>
      <th>Office</th>
      <th>Name</th>
      <th>Month</th>
      <th>Quantity</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>1a</td>
      <td>Abe D</td>
      <td>Jan</td>
      <td>10</td>
    </tr>
    <tr>
      <td>1a</td>
      <td>Abe D</td>
      <td>Feb</td>
      <td>13</td>
    </tr>
    <tr>
      <td>1a</td>
      <td>Jon R</td>
      <td>Jan</td>
      <td>9</td>
    </tr>
    <tr>
      <td>1a</td>
      <td>Jon R</td>
      <td>Feb</td>
      <td>12</td>
    </tr>
    <tr>
      <td>2b</td>
      <td>Eve C</td>
      <td>Jan</td>
      <td>13</td>
    </tr>
    <tr>
      <td>2b</td>
      <td>Eve C</td>
      <td>Feb</td>
      <td>14</td>
    </tr>
  </tbody>
</table>

<button>Filter</button>

.each()循环应该在行上循环。
然后使用.find()从行中获取name和month字段，测试它们，如果它们不匹配，则隐藏行。

$(document).ready(function() {
  var names = ["Abe D", "Jon R"];
  var mth = "Feb";

  $("button").click(function() {
    $("tbody tr").show(); // show everything before filtering
    $("tbody tr").each(function() {
      let tr = $(this);
      let mths = tr.find('td:nth-child(3)').text();
      let name = tr.find('td:nth-child(2)').text();
      if(!names.includes(name) || mths !== mth) {
        $(this).hide();
      }
    });
  });
});

<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<table>
  <thead>
    <tr>
      <th>Office</th>
      <th>Name</th>
      <th>Month</th>
      <th>Quantity</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>1a</td>
      <td>Abe D</td>
      <td>Jan</td>
      <td>10</td>
    </tr>
    <tr>
      <td>1a</td>
      <td>Abe D</td>
      <td>Feb</td>
      <td>13</td>
    </tr>
    <tr>
      <td>1a</td>
      <td>Jon R</td>
      <td>Jan</td>
      <td>9</td>
    </tr>
    <tr>
      <td>1a</td>
      <td>Jon R</td>
      <td>Feb</td>
      <td>12</td>
    </tr>
    <tr>
      <td>2b</td>
      <td>Eve C</td>
      <td>Jan</td>
      <td>13</td>
    </tr>
    <tr>
      <td>2b</td>
      <td>Eve C</td>
      <td>Feb</td>
      <td>14</td>
    </tr>
  </tbody>
</table>

<button>Filter</button>