If one includes a name of a person with a chronic disease (eg a cancer) in one’s ’refaenu’ prayer in the shemone esrea, and subsequently BEH the person recovers, or goes into remission, or tests come back negative, can/should one still mention that name in that prayer?

If the sick has become well again one should obviously give thanks to Hashem. One can always mention the name of someone in order that he may retain his good health and not become ill again. Rabbi Ro'i Margalit