The sender’s name will be associated with the text bubble that immediately follows within the same conversation. Currently, the name isn't being associated with the blue bubble because each of your lines is being formatted as separate text conversations. The brackets on the left and right edges show where each conversation begins and ends.
If you're converting text that is already present in the content editor to a text message conversation, you'll want to highlight the entire conversation and then press the text message button. Then, you can assign each line of the conversation to incoming message, outgoing message, or as the name of the person sending the message.
If you are typing a text conversation in Atticus, you can simply press Enter between each line to move to a new bubble or add the sender information.
Either of these methods will ensure that each part is contained within a single set of brackets in the editor and Atticus will then recognize them as parts of a single conversation.