Heading Tag for site display name

No, AFAIK, We can't change Appian's site internal definition - that level of customization is not allowed. You might mimic the Appian site UI using custom interfaces instead.

As Shubham clarified, no current direct way - though if you have a strong enough use case, and can demonstrate a method of configuration and potential Appian-side configuration that would be flexible overall, feasible for them to implement, and generally useful to appian designers everywhere, I'd urge you to submit a use case with Appian (sadly the only way to do this "officially" is via an Appian Support case, or to whine enough here on Community i guess).

For what purpose? I mean, you can easily add a header to the page and make it H1.