Given that you are working with AdventureWorks, I take it that this is not real task, but something you have made up on your own, and I will answer from this presumption.
The answer is that you do normally do these sort of things, because there is rarely any reason to in a well-designed normalised database.
A table in a relational database is supposed to model a unique entity, and from that perspective, each table needs its own code. Yes, two tables may have columns with same name, but they are still different entities.
And the SQL language is designed from this perspective. If you have two unrelated tables, you write two unrelated stored procedures. Yes, they may at this point look the same, but as a system evolves, they may grow apart by time.
You cannot say "UPDATE @tblname" and update different tables at different time. You can build SQL statements dynamically, but that is an advanced feature and not apt for beginners.