My first association with a tag such as "self-hosting" is @HOME and other such DIY which is off-topic for ServerFault.

Since questions regarding the polar opposite, shared web hosting, are usually already off-topic and there are already specific tags for most of the large cloud service providers such as amazon-web-services and others the label doesn't add anything for me.

When people manage web servers usually tag the question with the relevant specific apache-2.2, apache-2.4, iis, iis-8.5, nginx and such tags which is usually sufficient that to indicate what stack they are using on the server(s) they manage.

IMHO the typical business jargon would also be "on premise" if you really need to distinguish that you're not using a cloud/hosted version

My first association with a tag such as "self-hosting" is @HOME, DIY and an amateur approach, rather than managing information technology systems in a business environment which makes it off-topic for ServerFault.

Since questions regarding the polar opposite, shared web hosting, are usually already off-topic and there are already specific tags for most of the large cloud service providers such as amazon-web-services and others the label doesn't add anything for me.

When people manage web servers usually tag the question with the relevant specific apache-2.2, apache-2.4, iis, iis-8.5, nginx and such tags which is usually sufficient that to indicate what stack they are using on their server(s).

IMHO the typical business jargon would also be "on premise" if you really need to distinguish that you're not using a cloud platform.