我觉得不应该翻译成“谁该被管理”，而应翻译成“该由谁来管理”。

你的句子中的 govern 后面没有接宾语，说明它是不及物动词，下面是词典上的类似例子，其翻译供可参考：

In Great Britain the queen does not govern. 在英国，女王不执政。

They were utterly unfit to govern. 他们完全不胜任管理。

Who should govern? 在网上电子词典例句里，翻译成“谁该被管理=Who should be governed？” 

请问为什么？不应该理解为“谁应该来管理？”才对吗?

govern vt./vi统治；支配；管理；规定；控制

A: 主语+govern( 不及物动词用法）

In Great Britain the sovereign does not govern.   
在英国,君主不管理国家。

We have a queen, but it is the prime minister and cabinet who govern.   
我们有女王,但是首相和内阁执掌政务。

A king governs in that country.   
那个国家由国王统治。

Who are the men who really govern in this country?   
谁是这个国家的真正统治者?

B: 主语+ govern+宾语（及物动词用法）

You should govern your temper.你应该控制你的情绪。

The President governs the country.   
那个国家由总统统治。

A man who governs a state is a governor.   
管理一个州的人是州长。

They knew that his views on governing the country served the common people.   
他们知道他的治国思想就是为老百姓。

One can't completely govern his thoughts at all times.   
一个人不能始终控制得住自己的思想。

I appeal to you to govern your passions.   
我要求你们克制感情。

You should govern your temper.   
你应当克制你自己的脾气。

You should govern your conduct.   
你应当约束自己的行为。

The need for money governed all his plans.   
对钱的需求影响了他所有的计划。

This is the law governing the development of economy.   
这是经济发展的规律。

govern 主要有以下2个意思

(1)vt.统治；治理 （英文解释：To govern a place such as a country, or its people, means to be officially in charge of the place, and to have responsibility for making laws, managing the economy, and controlling public services.）

They go to the polls on Friday to choose the people they want to govern their country... 

星期五，他们去投票站投票选择他们所期望的国家管理者。

Their citizens are very thankful they are not governed by a dictator.  

他们的公民十分庆幸没有受独裁者的统治。

(2)vt.支配；控制；影响 （英文解释：If a situation or activity is governed by a particular factor, rule, or force, it is controlled by that factor, rule, or force.）

Marine insurance is governed by a strict series of rules and regulations.

关于海险有一系列严格的规章制度对其作了规定。

The government has altered the rules governing eligibility for unemployment benefit. 

政府已经修改了有关领取失业救济金资格的规章制度。