Squarespace provdes an option to change logo on mobile device only, with site title, you will need to use CSS code.
To update site title to another text on mobile device, you can use this code to Website Tools > Custom CSS.
div.header-display-mobile a#site-title {
visibility: hidden;
}
div.header-display-mobile a#site-title:before {
visibility: visible;
content: "New Mobile Text";
font-size: 22px;
line-height: 20px;
display: inline-block;
position: absolute;
top: 50%;
transform: translateY(-50%);
}
Result