Add these codes to the Custom CSS box and Save 

Rename Login text

/* rename login text */
span.unauth {
    visibility: hidden;
}
span.unauth:before {
    visibility: visible;
    content: "new login text";
    display: block;
}

The result like below

Login size on Mobile 

/* Login size on mobile */
div.header-menu span.unauth {
    font-size: 30px !important;
}

Result:

Login Text to icon

/* Login text to icon */
span.unauth {
    background-image: url(https://cdn.pixabay.com/photo/2024/01/19/18/00/hydrangeas-8519528_1280.jpg) !important;
    color: transparent !important;
    background-size: cover;
    background-repeat: no-repeat;
    background-position: center center;
}

You will have the result like this