Yes. In fact, UV 400 lenses are the maximum UV protection that sunglasses can provide. If your sunglasses are UV 400, it means you can get a very high level of eye protection through the sunglasses lenses. Besides, there are some sunglasses that may sign with "98% UV protection", "99% UV protection", they are the best sunglasses for shielding eyes from harmful UV sun rays.
I think UV400 is enough. These kinds of sunglasses can block UV rays with wavelengths up to 400 nanometers. Your eyes are shielded from even the tiniest UV rays when you are wearing this kind of sunglasses. You can also look for the label or a sticker which has the following words: lenses block 99% or 100% of UVB and UVA rays. Hope you can choose a pair of sunglasses that you like. I heard that the sunglasses sold by Firmoo on the internet are very cheap but with great quality at the same time, so I bought two pair of glasses on it. They are quite good. I like them very much. So I suggest you to have a look. But I have to admit that sometimes it will take you a long time to get the products for the transshipping is not very convenient sometimes. But I still think the products is worthy of our waiting.
Actually, UV 400 protection can block light rays with wavelengths up to 400 nanometers, which means that your eyes are shielded from even the tiniest UV rays. So the sunglasses with UV400 are really good sunglasses if you are looking for protection.