If I inherited stock do I only pay taxes on the amount of gain I acquired from the time the stock was transferred to my name till the time I cashed it out?

Your basis in the stock is the market value as of the date of death of the decedent you inherited it from which may not be the same date the stock was finally titled in your name.   Sale price - basis =  cap gain or loss and it will always be considered Long Term. 

Technically, the valuation date is the date of the previous owner's death.  I assume it took a couple of weeks to get a death certificate and notify the broker, the broker should back-date the valuation for you.  If not, you may need to research it.  Most of the time, stocks don't change much over a week or two, but the market has been strange lately.