What's in a name: Joseph

There are two Hebrew verbs that I often get mixed up:  אכפ (aleph-samekh-peh) which has a basic meaning of "gather, take away, assemble, withdraw;"  and יספ (yod-samekh-peh) which means "add, continue, do again, increase."   Because aleph and yod are both weak letters, they can drop out or change depending on the particular conjugation or meaning of the verb, so there are forms of each that look very much alike.  As well, yod is the verbal prefix for a certain type of verb.

 I confess, I almost always have to look them up.  Or go from context.

So which one is the source of Joseph's name?  Gen 30.23-24 from the NRSV:

23 She conceived and bore a son, and said, “God has taken away my reproach”;  24 and she named him Joseph, saying, “May the LORD add to me another son!”

Both!  I don't know if this is a combination of 2 separate traditions? or if they were just covering all their bases.  Or maybe the 2 verbs were originally the same word?  Hard to know.