Some Coleus are bred to have the most spectacular colors in mostly shade, and some will look faded if they are not in mostly sun. If you are able to add a pic of your Coleus, somebody may recognize it, but know that there are thousands of named cultivars. Those bred to be the most spectacular in the shade are going to look washed-out in too much sun, and in some cases, the variegation can be lost in too much sun, yielding just a solid color of leaf.
If you have multiple individuals, the process can be greatly accelerated since you can experiment with multiple exposures at the same time.
If you do not want to sacrifice the size of your plant, you could give it a gradual adjustment, first to shade, then into a bit more sun in the morning or late afternoon, over the course of a month or so, and you should be able to find the tolerance of your plant and the exposure that shows the colors that you most appreciate, even if a specific cultivar name remains elusive. Agree that even if there is some sunburn, it will be very temporary. Coleus grow new leaves very quickly.
The terms that I see most often for this kind of adjustment are acclimation and if the plants are seedlings, hardening-off.