[Dr.CustUmz]

Animating a gradient using a small percentage might do the trick, if this doesn't point you in the right direction and I find some time I might type something out.

--------------- Added [DATE]1614636808[/DATE] at [TIME]1614636808[/TIME] ---------------

Animations are not my thing, but this is a little closer to your desired effect. took me a whole 2 minutes to type up, and only played with the positioning for a minute before I got over it, a little fiddling I'm sure you can get it perfected how you want it.

<h1 class="username animated">DrCustUmz</h1>

.username {
    text-align: center;
    font-size: 25px;
}
.animated {
    background: linear-gradient(to right, #ff0000, #000);
    -webkit-background-clip: text;
    background-clip: text;
    color: transparent;
    animation: animation 15s linear infinite;
    background-size: 20%;
}

@keyframes animation {
    0%,100% {
        background-position: 10%;
    }

    99% {
        background-position: 100%;
    }
}

--------------- Added [DATE]1614637794[/DATE] at [TIME]1614637794[/TIME] ---------------

Exact effect, Figured out a way but dont thing it would be possible for a username, not easily atleast.

<div class="username">
  <span>D</span>
  <span>r</span>
  <span>C</span>
  <span>u</span>
  <span>s</span>
  <span>t</span>
  <span>U</span>
  <span>m</span>
  <span>z</span>
</div>

.username > span {
  text-transform: uppercase;
  animation: flash 2s ease-in-out infinite;
}

@keyframes flash {
  0%, 100% {
    color: #FF0000;
  }
  
  10%, 90% {
    color: #000;
  }
}

.username > span:nth-child(2) {
	animation-delay: 0.25s;
}

.username > span:nth-child(3) {
	animation-delay: 0.5s;
}

.username > span:nth-child(4) {
	animation-delay: 0.75s;
}

.username > span:nth-child(5) {
	animation-delay: 1s;
}

.username > span:nth-child(6) {
	animation-delay: 1.25s;
}

.username > span:nth-child(7) {
	animation-delay: 1.5s;
}

.username > span:nth-child(8) {
	animation-delay: 1.75s;
}

.username > span:nth-child(9) {
	animation-delay: 2s;
}