I am attempting to alter an existing stored procedure with the command
ALTER 'name_of_stored"procedure'
however the name is highlighted in red noting it is an invalid object. I am able to execute the command successfully however am wanting to know why SQL Server 2008 R2 notes it as an error.
It's SSMS, not SQL Server. If it's an error against the database engine you'll know it (it wouldn't execute the command successfully).
You need to refresh the Intellisense cache (Ctrl + Shift + R). Or you can go to Edit -> IntelliSense -> Refresh Local Cache.