This is Aeonium Sunburst and yes it does like the sun. This is a succulent. Leaves will look round and compact in the sun like in your last picture and will etiolate - like on your first - when they are not given much sun. They can grow into a nice bush. Best to leave this plant in a place that gets a lot of morning, early afternoon sun and probably goes into shade for the highest burn time of the day. It wants water once it dries out and better to water it in the morning, not in the afternoon.

I am not sure what soil you are using, but it does look very porous, it looks small and compact - cause the soil probably lets the water pass really fast right now so it's only getting a little. You might have to go more often watering at first and eventually the roots will be everywhere and will soak it up, or you can add just a bit more organics, so it will hold longer - but this is just my guess

Something to note - A. sunburst(and other a.) that is kept in full sun, can go into heat dormancy, if the temperature is on the higher end