I want to display the sender's name rather than their contact photo within a text message conversation I want to display the sender's name rather than their contact photo within a text message conversation.  I don't have everyone's contact photograph memorized and I have multiple people with the same contact photograph.  My old Android (version 4.0.4) did display the name within the conversation bubble, my new one (version 4.3) displays a small contact photograph next to the conversation bubble instead of the sender's name.  One friend has some random cat wearing sunglasses as her contact photo....I certainly don't associate that with her and when she changes her contact photo then there will be some other random thing I don't associate with her.  I would prefer to see her name rather than a random cat.  For people who don't have a contact photo or for whom I don't have a photo, it displays a generic outline of a head.
I recommend installing an alternative SMS app. Once you have it downloaded you won't need any Internet connection. From your comment


  "Apps work great when you have a good connection to 4G, 3G, etc." 


you are obviously concerned about Internet speed, but this isn't an issue for an app that sends SMS. It will send and receive your text messages in place of the app you are currently using. I do not mean an Instant Messaging application like Kik or Whatsapp, I mean a dedicated SMS app. The current app you use is provided by whoever made the device (e.g. Samsung or HTC or Sony) and it works in its own way. 

By way of an example here is a shot of Google Messenger  where you can see the name at the top of each conversation. 



Note: This won't be compatible below Android 4.1 JellyBean so will not suffice in this specific instance, but may be of use to others on the site. 

Another good SMS app is Go SMS Pro which is also free on the Play Store. 

Google Hangouts can also be used for SMS. There are many great SMS apps on the store, and I'm sure at least one of them will suffice.