The step to rename the database is quite straightforward. Look here:
ALTER DATABASE [dbname] MODIFY NAME = [newdbname]
http://azuregeek.com/how-to-rename-database-in-sql-azure[
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As far as the impact is concerned, it's impossible to tell from here.
Start asking questions to your colleagues and other application admins, such as which application(s) are using this database. Where is the connection string defined? Who is going to take care of that?