What is the area of ​​the nail called?

…and does anyone of you know how to take good care of this area?

This isn't my finger, just a sample picture. I often have bits of skin hanging off it, and if I clip them off , it eventually grows back . And, above all, the red, clipped-off part doesn't look very attractive.

I've always had a problem with this, and it's been bothering me for a while. It would be nice to find a solution.

The two hand creams I've tried so far have n't made a difference for me. I would be grateful for any recommendations .