I asked Firebase support and got the following reply. Items in italics are my additions.
In order to update firebase-project-id.firebaseapp.com in the OAuth consent screen, you need a custom domain with Firebase Hosting (Firebase Console > Hosting > Connect Domain). This is because https://firebase-project-id.firebaseapp.com/__/auth/handler is hosted by Firebase Hosting. You need to point your custom domain to firebase-project-id.firebaseapp.com .

• When connecting the custom domain, if you are not hosting your app on Firebase, use a new subdomain (e.g. app.yourdomain.example ) and do not redirect it. Firebase will prompt you to add an entry on your DNS server and take care of the SSL certificate automatically.*

After connecting your custom domain to your Firebase project, you should also follow the steps below:

1. Go to the Firebase Console > Select Project > Authentication > Sign-in method > Facebook > Copy the URL under 'To complete setup, add this OAuth redirect URI to your Facebook app configuration.'

• It will look something like https://firebase-project-id.firebaseapp.com/__/auth/handler

1. Replace the project ID with your custom domain. It will look something like: https://yourdomain.example/__/auth/handler
2. Go to the GCP Console > Select project > API Manager > Credentials > Add the link in #2 to the 'Authorized redirect URIs'
3. Then ensure to use yourdomain.example as the authDomain in your app's configuration instead of firebase-project-id.firebaseapp.com

firebase.initializeApp({
     apiKey: ....,
     authDomain: 'yourdomain.example',
      ...
 });

In my case, yourdomain.example is where I host my site, so I used app.yourdomain.example where I needed it.

• Firebase Hosting URL
• handler URL: https://app.yourdomain.example/__/auth/handler
• GCP Credentials
• Choose the right one under OAuth 2.0 client IDs. The client ID will match the one you have configured Firebase with in your code.
• authDomain: "app.yourdomain.example"

这就是我的工作：
1.将代码中设置的Firebase配置更改为authDomain: "insertyourdomainnamehere.example"
1.按下应用程序上的“登录Google”，查看由于此更改而出现的错误。按照错误说明进行操作。
错误导致我到https://console.cloud.google.com/apis/credentials（谷歌云平台〉API &服务〉凭据）.
1.在该页面上，查看“OAuth 2.0客户端ID”部分。
1.对我来说，只有一个记录“Web客户端（由Google服务自动创建）”。单击上面的编辑按钮。
1.查找“授权重定向URI”部分。在该部分中，添加：https://insertyourdomainnamehere.example/__/auth/handler .
然后它应该工作！它现在应该说“登录以继续yourdomain.example”。

对于我的情况下，Web应用程序与电子邮件登录，我只需要进入控制台上的项目设置，在general选项卡下更改Public-facing name和电子邮件中的%APP_NAME%得到更改

你应该在Google API控制台（https://console.cloud.google.com）中进行这些修改。在那里，找到你的项目证书，点击“OAuth同意屏幕”，然后出现一个文本框，上面写着“向用户显示产品名称”，将当前名称更改为你的应用名称，然后点击“保存”。

我想我可能找到了为什么有些人可以更改显示名称而有些人不能。请检查“托管”选项卡。如果您部署了某个内容，它可能部署到了登录页面上列出的同一个URL。请尝试在该页面上添加您的域名，看看是否有效。

这个帮助页面相当全面-但是你必须做的一件关键事情是在你的firebase.config()设置中修改authDomain参数。
但是如果你在web上使用他们的"easier configuration"作为firebase，你只是加载/__/firebase/3.7.4/init.js而没有指定配置，那该怎么办？因为它是自动处理的，有没有办法只修改配置的authDomain部分？