Temporarily Archive Databases on SQL Server 2008 R2
To answer your questions first:


  What are the potential pitfalls with temporarily renaming a database?


At this scale, it'd be bothersome and just potentially messy to be renaming this many databases multiple times in the case some are needed. It may be a pain cutting off all connections when re-naming and could confuse other users as well.


  Does MSSQL remove any logins or authentication information when a
  database is renamed and then renamed back?


Nope! Not an issue.


  Does anyone have a more standardized recommendation for this process,
  or a direction to point me to get me researching further?


In this case, I'd probably just take the databases OFFLINE temporarily to see if they are needed.

You can do this via the GUI by right-clicking a database, Task -&gt; Take Offline, or via TSQL:

ALTER DATABASE [dbname] SET OFFLINE;

When a database is offline, all connections are closed and no new connections can be made to it. It's quick to bring it back online if required:

ALTER DATABASE [dbname] SET ONLINE;

Plus, when the database is offline it's using less resources than an online database, so it may be better for performance in the mean time as well.