What can i do if even dove soap leaves my hands dry and rough?

Since you should be performing hand hygiene frequently in this era of COVID, one suggestion is to deep moisturize at night, after washing, with white petrolatum, or cocoa butter, or even solid shortening (Crisco).

After washing your hands' use a skin moisturizer. See a doctor, there are also possible dermatitis or fungal infections which can cause this.

The first thing to do is try other brands of soap to see if the hands are less rough. One can also use hand lotions . If one is not satisfied by these efforts, then a visit with the Dermatologist is in order.

Agree with Dr. H. You may try liquid hand soap with moisturizer. As advised by other, using emollient will be helpful. Have a healthy diet, exercise 30 minutes/day, drink plenty of water daily so your urine is mostly colorless, have safe sex, no tobacco alcohol weed or street drugs. For nutrition: http://www.choosemyplate.gov/.