Я думаю, что это невозможно с фоном. Другой альтернативой является рассмотрение mask
с использованием SVG, где вы применяете вращение. В маске будет текстовое содержимое:
#rotating-c {
width:200px;
height:200px;
display: inline-block;
-webkit-mask:url('data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" version="1.1" viewBox="0 0 13 13"><style>text { transform-origin:center; animation:change 5s linear infinite;} @keyframes change { from {transform:rotateY(0deg)} to { transform:rotateY(360deg); }}<\/style><text x="0" y="12" font-family="Arial, Helvetica, sans-serif" transform-origin="center">C</text></svg>') center/contain;
mask:url('data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" version="1.1" viewBox="0 0 13 13"><style>text { transform-origin:center; animation:change 5s linear infinite;} @keyframes change { from {transform:rotateY(0deg)} to { transform:rotateY(360deg); }}<\/style><text x="0" y="12" font-family="Arial, Helvetica, sans-serif" transform-origin="center">C</text></svg>') center/contain;
background-image: url(https://images.freecreatives.com/wp-content/uploads/2015/10/free-space-textures.jpg);
}
<div id="rotating-c">
</div>

У вас также может быть много букв для создания слова с использованием нескольких масок:
#rotating-c {
width:600px;
height:150px;
display: inline-block;
-webkit-mask:
url('data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" version="1.1" viewBox="0 0 13 13"><style>text { transform-origin:center; animation:change 5s linear infinite;} @keyframes change { from {transform:rotateY(0deg)} to { transform:rotateY(360deg); }}<\/style><text x="0" y="12" font-family="Arial, Helvetica, sans-serif" transform-origin="center">A</text></svg>') 0 0,
url('data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" version="1.1" viewBox="0 0 13 13"><style>text { transform-origin:center; animation:change 5s linear infinite;} @keyframes change { from {transform:rotateY(0deg)} to { transform:rotateY(360deg); }}<\/style><text x="0" y="12" font-family="Arial, Helvetica, sans-serif" transform-origin="center">F</text></svg>') 33.33% 0,
url('data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" version="1.1" viewBox="0 0 13 13"><style>text { transform-origin:center; animation:change 5s linear infinite;} @keyframes change { from {transform:rotateY(0deg)} to { transform:rotateY(360deg); }}<\/style><text x="3" y="12" font-family="Arial, Helvetica, sans-serif" transform-origin="center">I</text></svg>') 66.66% 0,
url('data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" version="1.1" viewBox="0 0 13 13"><style>text { transform-origin:center; animation:change 5s linear infinite;} @keyframes change { from {transform:rotateY(0deg)} to { transform:rotateY(360deg); }}<\/style><text x="0" y="12" font-family="Arial, Helvetica, sans-serif" transform-origin="center">F</text></svg>') 100% 0;
-webkit-mask-size:150px 100%;
-webkit-mask-repeat:no-repeat;
mask:
url('data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" version="1.1" viewBox="0 0 13 13"><style>text { transform-origin:center; animation:change 5s linear infinite;} @keyframes change { from {transform:rotateY(0deg)} to { transform:rotateY(360deg); }}<\/style><text x="0" y="12" font-family="Arial, Helvetica, sans-serif" transform-origin="center">A</text></svg>') 0 0,
url('data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" version="1.1" viewBox="0 0 13 13"><style>text { transform-origin:center; animation:change 5s linear infinite;} @keyframes change { from {transform:rotateY(0deg)} to { transform:rotateY(360deg); }}<\/style><text x="0" y="12" font-family="Arial, Helvetica, sans-serif" transform-origin="center">F</text></svg>') 33.33% 0,
url('data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" version="1.1" viewBox="0 0 13 13"><style>text { transform-origin:center; animation:change 5s linear infinite;} @keyframes change { from {transform:rotateY(0deg)} to { transform:rotateY(360deg); }}<\/style><text x="3" y="12" font-family="Arial, Helvetica, sans-serif" transform-origin="center">I</text></svg>') 66.66% 0,
url('data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" version="1.1" viewBox="0 0 13 13"><style>text { transform-origin:center; animation:change 5s linear infinite;} @keyframes change { from {transform:rotateY(0deg)} to { transform:rotateY(360deg); }}<\/style><text x="0" y="12" font-family="Arial, Helvetica, sans-serif" transform-origin="center">F</text></svg>') 100% 0;
mask-size:150px 100%;
mask-repeat:no-repeat;
background-image: url(https://images.freecreatives.com/wp-content/uploads/2015/10/free-space-textures.jpg);
}
<div id="rotating-c">
</div>
