I've been doing Centering Prayer as taught by Fr Keating, for over 40 years now.
It was originally called, "Quiet Prayer," or "Prayer of Quiet," which goes back to
the forth century mystics like Abba Isaac and St John Casein.
See the 1917 Catholic Encyclopedia,...............
CATHOLIC ENCYCLOPEDIA: Prayer of Quiet
The term became Centering Prayer when Fr Keating and Fr Pennington were giving
a retreat to religious. The focus was on Thomas Merton's writings on St John of the
Cross where he used the term, "Centering," so much, that as the retreatants talked
and asked questions about it, they just started to call it "Centering Prayer." The term
stuck, but became negative as people misinterpreted what it was and thought it was
what the New Age movement called "centering." They are not the same.
Emptying is merely emptying oneself of thoughts and ideas which have nothing
to do with being present in prayer. Centering Prayer is the beginning of Contemplative Prayer or as St Teresa of Avila called it, "Interior Prayer."
A good book to read on this in addition to Fr Keating's, is "Into the Silent Land," by
Fr Martin Laird. In the book he uses the original term, "Quiet Prayer," for as he wrote,
"Centering Prayer," means different things to many people.