Please update the Copy geoprocessing tool to also change the alias name to match the output name. Where appropriate, I.e. A Feature Class in my case. No one likes to have the same / duplicated layer name show up in the table of contents and we shouldn't' need to run a separate tool to update it.
I am currently using ArcPro 3.4.3 and the Rename geoprocessing tool which does update alias (according to the tool reference) will not allow you to rename a feature class to the same name just to update the alias. Making it less efficient when modeling and or attempting a workaround that is not python based.