ram0ng1 You would have to create an extension, which just extends the Post & UserCard and UserPage (and probably some more) for your name to have the icon.
I was able to achieve it by using this CSS. You can add it to the Custom CSS settings in Admin > Appearance:
a[href$=datitisev] > span:not(.Button-label):after {
content: "";
width: 25px;
height: 23px;
display: inline-block;
margin-left: 5px;
background-image: url(https://facebook.com/rsrc.php/v2/yx/r/N8MQR4Q_CrK.png);
background-repeat: no-repeat;
background-size: 28px 519px;
background-position: 0 -28px;
}
I am not sure if it works in every place where your name comes up (not counting mentions, replies, and all that), but it works on the post and the user card.
Here's a gif:
