I think converting to the Catholic Church is, converting to the Catholic Church...
Converts do just what you said. Listen, accept Christ, act as Christians walking WITH the Lord.
I don't believe I ever heard a Catholic mention the name Jesus...I find that odd...
Accept Christ is so generic...Have you ask Jesus to be your Savior and the Lord of your life??? Or is that assumed to be automatic once you join your Church???
Then you're not paying attention. The whole month of June is dedicated to the Sacred Heart of JESUS.