Yes, it is Sphaerodactylus elegans or the Ashy gecko and you are quite lucky. Try feeding it flightless fruit flies (Drosophila melanogaster). Just put some a drop of non-citrus fruit baby food in the bottom and the flies will stay near by. You should be able to buy a culture of the flies at a "specialty" pet store if you cannot find one their are online dealers. Mist the enclosure atleast twice a day. Once the animal readily feeds on the flies, you need to add a calcium supplementation for correct bone formation. Exposure to UVB rays helps them process calcium. However if the animals doess not receive atleast 2-3 hours of natural sunlight or an indoor plant light or reptile light with UVB, vitamin D3 should only then be part of any calcium supplementation. The temperature should be around 85F daytime and 75-78F night time. Humidity should stay around 65-80% with breif periods of 100% (after misting). Good ventilation is necessary, however, you need to keep it in an ant/spider proof enclosure. I would temporarily use a small mason jar (pint-quart) with the middle piece of the lid replaced by a fine screen (the kind coated with black should work well). For subtrate, the commercial Jungle Mix would be best. The more naturalistic the better when it comes to getting it used to captive care. It is young so it is probably not stuck in it ways yet.
Good Luck,
Ashton