I have a windows machine with IIS and I can see the IIS welcome page on http://myname/
. I have recently started using Shiny through its own server and I can see
The comments have already said this, but in the interest of providing an answer:
You can use shiny server (free and pro) to host apps on your own server. I believe this will allow you to set it up on http://myname/, however shiny server should be running in a linux environment as listed by @pops.
https://www.rstudio.com/products/shiny/shiny-server/
Or
you can use shiny.io to host them for you, with premium versions having the ability to set your own domain
https://www.shinyapps.io/