Custom drums, I don't think there's any yet. That is, if you're thinking of things like those companies overseas where you can place orders and they send it to you. I think this is mainly because the start-up cost is really high, you'll need a workshop and expensive equipment, and it's probably harder to get the raw materials in Singapore.
However, there are Singaporean brands, if I remember right, Carlos is a Singaporean brand that does budget drums.
Also, there's people who DIY stuff for themselves. I've seen at least one member here who put together drums from parts ordered online. Me and Jeepers are also intending to do that.
Myner here hammers cymbals. You can ask him about that.
There's also refinishing. I've done dyes/lacquers, and rewrapping, using materials bought locally from hardware stores and so on. I've seen another member here do it with wood-print wallpaper, and I've heard of other people in Singapore who do it also.