How do I arrange confession as a hospital inpatient?

Call the spiritual care or chaplaincy office and use the word priest.

This wording matters. Only a priest can hear a confession and give absolution. Hospital chaplaincy teams include deacons and lay chaplains who can pray with you and bring Communion but cannot absolve you, so a general request for a chaplain may not reach the right person. Ask when a priest is next on site, and what the arrangement is outside normal hours.

If you are in a Catholic facility, the Directives place an obligation on the institution here: "Particular care should be taken to provide and to publicize opportunities for patients or residents to receive the sacrament of Penance."

Privacy is a fair thing to ask for. A shared bay is not a confessional, and asking staff for the curtain to be drawn, or for a roommate's visitors to step out for a few minutes, is an ordinary request that they will help with.

If you have been away from the sacrament for a long time, you do not need to explain that on the phone, and it is not a screening question. Priests who do hospital work spend much of their time with people in exactly that position.