Differential Backup from SQL Server 2012 to Azure Blob
You are correct, this is not possible in Azure cloud. You can do this for premise backup which I highly discourage. It just makes your restore more complicated. But in Azure if file name already exists in your container only way to use that same name is to use WITH FORMAT which will create a new media set.

I tested this and I get following error message:


  Msg 3296, Level 16, State 1, Line 1 The file
  https://storageacocunt/sqlbackfiles/testFull.bak
  exists on the remote endpoint, and WITH FORMAT was not specified.
  Backup cannot proceed. Msg 3013, Level 16, State 1, Line 1 BACKUP
  DATABASE is terminating abnormally.


From Books online:

BACKUP (Transact-SQL) | Microsoft Docs


  FORMAT 
  
  Specifies that a new media set be created. FORMAT causes the
  backup operation to write a new media header on all media volumes used
  for the backup operation. The existing contents of the volume become
  invalid, because any existing media header and backup sets are
  overwritten.


You can check this with RESTORE HEADERONLY command. If you take a fullbackup and then a differential WITH FORMAT, you will see backup type change from 1 to 5.

I suggest you create a new for each file.

This link has example about generating a new filename for each backup.