Name, Address, Name and Address
The address name is the name that's on the address, making it the addressee. This can also mean name and address.
This can be used for both physical mail and email.
The reading for 宛 is the same one you learned for the kanji. The reading for 名 comes from the kun'yomi reading, which you learned in the vocabulary word 名 and 名前. So, the reading for this word is あてな.
It looks like there is an error in this address.
I was entrusted with the task of writing names and addresses.
I lost the list of customer names and addresses.