Hello,
It looks like this is the Fakebook, a theme for social media lovers theme. Fakebook theme uses custom template on topic list to show username but you can modify this template to show the full name too. 
For this you need to fork the theme on Github and edit the template file. This is the file you have to modify on your fork. Fakebook/custom-topic-list-item.hbr at main · discourse/Fakebook · GitHub
This template has a section which handle user datas on topic list. You have to edit this.
This line shows the username. 
<span class="username">{{topic.posters.[0].user.username}}</span>
So we have to add the full name before or after this.
To add full name just simple change this section something like this
<div class="name-and-date">
<span class="full-name-topic-list">{{topic.posters.[0].user.name}}</span>
<span class="username">{{topic.posters.[0].user.username}}</span>
{{format-date topic.createdAt format="tiny"}}
</div>
I added this line above username and this will show the full name on topic list, above username.
<span class="full-name-topic-list">{{topic.posters.[0].user.name}}</span>
Probably need some CSS change but you can easily target the full-name-topic-list class or whatever class you added.
I forked the Fakebook theme now and made this change in this commit so you can see it. Add full name to topic list · VaperinaDEV/Fakebook@0978133 · GitHub
And this is how it looks like.
Don - Full Name
dodesz - Username
Hope this helps