Is there any way to change the tableau server logo that appears in the browser tab?

Hello @Adam Levitt​ 

I would recommend creating a product idea for it.

Note I did find an old community question in relation to changing the favicon defined as A in the above link where the user mentions a possible solution. However I would have to add that as the official online help advised it is not customizable that this may not work / is not supported. So I would very much caveat that it is an "at your own risk"

https://community.tableau.com/s/question/0D54T00000CWeo3/website-icon-location