What is the name of this snake?
I'm not an expert by any means, and anyone with proper training could probably provide a more informed opinion, but here's my thoughts. The patterning looks similar to Oligodon taeniolatus, an small, nonvenomous snake found throughout the region:


I'm not entirely sure about this identification, mostly because the pattern on the head looks a bit different. Sri Lanka has a large diversity of snakes and finding an definitive identification might be difficult without better images. There seems to be only a handful of snakes considered deadly, and this doesn't appear to be one of them. However, as I said, I'm not an expert, and even if it's not one of the 'deadly' ones, that doesn't mean it couldn't be dangerous to small children or pets. If you intend to capture and release the snake away from the house, I'd still recommend caution when handling it or contacting a professional.