This is a great question, and I'm happy to see that you're interested in the customer experience here. The customers will see the supplier's address as the sender on the package, but otherwise, they should only see their own information as the recipient.
Are you using the Oberlo app to import AliExpress products to your store? If so, your customer's address will be automatically synced to your AliExpress order so long as you're logged into your AliExpress account and have the Oberlo Chrome Extension installed. You can find more details on the AliExpress fulfillment process here: How to Fulfill AliExpress Product Orders.
There are also some settings in your Oberlo dashboard that can be configured to ensure that your customers are not receiving any unwanted information. In the Suppliers settings, you can add your own phone number so that the customer isn't contacted about their order, and you can also leave a note for suppliers letting them know that you're dropshipping so that they don't include any flyers or invoices with the package.
Please let me know if you have any questions about this and I'd be happy to continue the conversation.
Aliexpress suppliers always put their own labels and promos in their shipments. From oberlo you can make a special note to supplier "I am a dropshipper do not include the product price, your promo materials."
Just go to Oberlo > Settings > Suppliers and add a custom note as shown here: http://take.ms/ph5d5.
If you want the supplier to include your brand logo, you should discuss it personally with them and make a deal OR you can use any private label suppliers but they cost higher.