One can manipulate output files in a PostBuildEvent element. In my original question I wanted to rename a content file, LICENSE. In my specific case I wanted to rename it to match the assembly, so as to avoid any collisions. I use github which requires license files be named LICENSE but I want the output to have a different name, hence my issue here. The following is the most simplified form. All of the magic happens in the *proj file:

<?xml version="1.0" encoding="utf-8"?>
<Project Sdk="Microsoft.NET.Sdk">
    <PropertyGroup>
        <AssemblyName>Foo</AssemblyName>
    </PropertyGroup>
    <ItemGroup>
        <Content Include="LICENSE" CopyToOutputDirectory="Always" />
    </ItemGroup>
    <PropertyGroup>
        <!--
            The following will rename the output file LICENSE
            to Foo.License.txt during the build process.
            It leaves the original source file intact,
            and only changes the output file.
            The PostBuildEvent runs in the context of
            $(OutDir)\$(Configuration)\$(TargetFrameworkVersion)
            Ex: bin\Debug\net6.0
        -->
        <PostBuildEvent>
            ren LICENSE $(AssemblyName).License.txt
        </PostBuildEvent>
    </PropertyGroup>
</Project>

The first thing to understand is the Content element. We're including the file LICENSE in the build output. This will get dumped in the usual place, $(OutDir)$(Configuration)$(TargetFrameworkVersion). Next we configure an arbitrary command to execute in the PostBuildEvent element. Stuff here will happen when the build process completes. The working directory is $(OutDir)$(Configuration)$(TargetFrameworkVersion). So in this case I've queued up a file rename operation.

Similarly one could delete files, or move them to places outside of the project directory, etc.

It should be noted that "ren" is a windows thing, so you might need to execute "mv" if you are using linux or mac. Sorry but I have no opportunity to explore those environments.