What does it mean to receive a fulness of the Holy Ghost?
I assume you are referring to D&C 109:15 “And that they may grow up in thee, and receive the fulness of the Holy Ghost . . . ”
Because Heavenly Father loves all His children, those who are members of His church, and those who are not, all who truly seek Him can feel the influence of the Holy Ghost. Consider C.S. Lewis, or Mother Theresa, surely they received some guidance from the Holy Ghost to help them in their service to others.
However, to receive the “fulness of the Holy Ghost” means to have His constant companionship. In order to receive that blessing one must be baptized and receive the gift of the Holy Ghost by priesthood authority. But it does not end there. After being given this blessing we have to remain worthy.
It is very important to have the Holy Ghost as our companion. He can comfort us in our trials and tribulations, teach us eternal truths and things we need as individuals, warn us of spiritual and physical dangers, and help us feel the love of Heavenly Father and Jesus. In short, the Holy Ghost sanctifies us.
Whether we receive these blessings is largely up to us. If we are willing as King Lamoni to give up all our sins to know Him (Alma 22:18) and endure to the end, we will receive the fullness of the Holy Ghost. That does not mean that we have to be perfect, what the Lord expects from us is to try, and repent when we fail and try again.