Steveorevo

Domain Theme allows you to specify more then one domain name with your WordPress installation and optionally associate a specific theme for each domain. This enables you to present your site under multiple domain names. (i.e. www.mypersonalblog.com and www.myprofessionalblog.com). A specific theme template can be assigned to a specific domain. For instance, you can use this plugin for a personal blog that has a casual theme under one domain and and present the same data under a corporate theme that omits select categories (i.e. family photos, etc.). You will need to modify your DNS settings to point your domain name(s) to the same server to make this happen.
Known Issues:
<ul>
<li>
Upgrade users from WordPress 2.6 to WordPress 2.6.1 who used version 1.2 may have incompatible domain data. Please delete and recreate your domain list.
</li>
<li>
All-In-One SEO users should delete their “Home title” setting otherwise it will overwrite the blog title settings in Domain Theme.
</li>
<li>
Please note that accessing wp-admin pages from any other domain name then your primary domain specified in ‘General Settings’ will cause the administration panel to report the ‘themed’ settings. Just remember to access your ‘General Settings’, ‘Presentation’, and ‘Domain Theme’ admin pages under your primary domain name if you want to make such changes.
</li>
<li>
Users before version 2.5 will have a minor UI issue on the Domain Theme control panel’s ‘delete all’ checkbox column. It will not check off all listed items.
</li>
<li>
The first item in the Domain Theme list cannot be deleted as it is the settings you have for your primary domain taken from the ‘General Settings’ and ‘Presentation-Theme’ page. Clicking it to edit will simply transfer you to the ‘General Settings’ page. This is on purpose.
</li>
<li>
Some users may have issues with their server variables SERVER_NAME versus HTTP_HOST. Simply uncomment the first line of code in the plugin if your additional domain names do not appear to work. See the comment on the first line of code.
</li>
</ul>

Domain Theme

Domain Theme allows you to specify more then one domain name with your WordPress installation and assign individual themes to each one.

jediconcepts

A WordPress plugin that adds unique favicon support for each domain mapping in the <a href="https://wordpress.org/plugins/multiple-domain-mapping-on-single-site/" rel="ugc">Multiple Domain Mapping on single site</a> plugin.
Plugin Repository: [https://github.com/jediconcepts/multi-domain-favicon-manager] 
Support: dev@jediconcepts.com
<h4>Features</h4>
<ul>
<li>Unique favicons per mapped domain – Set different favicons for each of your mapped domains</li>
<li>Media library integration – Upload new favicons or browse existing media</li>
<li>Smart domain conversion – Automatically converts URLs between base and mapped domains</li>
<li>Conflict resolution – Removes WordPress default site icons to prevent conflicts</li>
<li>Search functionality – Find favicon files by filename when media browser filters them out</li>
<li>Multiple file format support – Works with .ico, .png, .svg, .jpg, and .gif files</li>
<li>Auto-preview – See favicon previews when entering URLs manually</li>
</ul>
<h4>Requirements</h4>
<ul>
<li>WordPress 5.0 or higher</li>
<li>PHP 7.4 or higher</li>
<li><a href="https://wordpress.org/plugins/multiple-domain-mapping-on-single-site/" rel="ugc">Multiple Domain Mapping on single site</a> plugin (required dependency)</li>
</ul>
<h4>How It Works</h4>
Frontend Behavior 
When a visitor accesses a mapped domain:
<ol>
<li>Plugin detects the current domain mapping</li>
<li>Checks if a custom favicon is configured for that mapping</li>
<li>Outputs the custom favicon HTML tags</li>
<li>Suppresses WordPress default site icon to prevent conflicts</li>
</ol>
Admin Interface 
The plugin adds favicon management fields to each domain mapping:
<ul>
<li>Integrates seamlessly with the existing Multiple Domain Mapping interface</li>
<li>Provides intuitive upload and selection tools</li>
<li>Shows preview of selected favicons</li>
<li>Validates favicon URLs automatically</li>
</ul>
<h4>Button Functions</h4>
<ul>
<li>Upload New (Blue) – Upload fresh favicon files from your computer</li>
<li>Browse Media (Green) – Select from existing files in your media library</li>
<li>Search by Name (Orange) – Find specific files by filename when media browser doesn’t show all files</li>
<li>Convert URL (Purple) – Convert between base domain and mapped domain URLs</li>
</ul>
<h4>File Format Support</h4>
Supported favicon formats:
<ul>
<li>.ico – Traditional favicon format</li>
<li>.png – Modern format, recommended for most uses</li>
<li>.svg – Scalable vector format</li>
<li>.jpg/.jpeg – JPEG images</li>
<li>.gif – GIF images</li>
</ul>
Recommended size: 16×16 or 32×32 pixels

Multi-Domain Favicon Manager

Got to give this 5 stars

Unique favicon support for each domain mapping in Multiple Domain Mapping plugin.

Domain Theme vs Multi-Domain Favicon Manager