Where can I find my Azure account name and account key?

You can check it by using Azure CLI:

az login
az storage account list -o table
az storage account keys list -n YourAccount

To extract the first key, you can use the following command:

az storage account keys list -n YourAccount -o json --query "[0].value"

The user interface changed a little bit but it's generally the same place:

Note that on the right side of the key you have a Connection String. There you can clearly see the name and the key as well.

If you're referring to a Windows Azure Storage account, the storage account name would be the dns prefix you created (e.g. mystorage.blob.core.windows.net - the name would be mystorage).

You then get two keys - primary and secondary. Specify either. You have two so you can give one out to someone (such as giving the secondary key to a 3rd-party monitoring company) and revoke it by changing the key, without impacting you (assuming you're using the primary key for yourself).

Adding a new answer as Azure UI is updated.

So, after selecting the storage account(in my case its inAFlash) select Access keys option you will get the following screen shown in the screenshot

Here you see two key's Primary and secondary. So, previously these were key1 and key2.

Reason for two keys? it's to avoid downtime. let's say, if you had only one key and used it multiple places. Suddenly you had to share it to someone for some reason. So, you might need to regenerated this key(As you have already shared it) and update it in all places where you used it previously. So, to avoid this, we have secondary key, which you can share and regenerate it so that, primary key will be still valid.