Is that necessary to use only one toothpaste for teeth ?

Toothpaste: Almost any toothpaste will be adequate. Actually you don't have to use a toothpaste when unavailable as long as you brush and floss properly. I would recommend any major brand toothpaste with Fluoride and avoid the whitening toothpastes on a regular basis as they are generally too abrasive. Eat healthy as well.

Yes only teeth: Yes, toothpaste should only be used for teeth and not on any skin because it can irritate and possibly burn the skin.