WASHINGTON (AP) _ Nancy Reagan paid her final Christmas visit to Children's Hospital National Medical Center as first lady Wednesday, but she left her name behind on adolescent recreation room.

''For Children's Hospital, for the children and the staff here Christmas really begins when Mrs. Nancy Reagan comes and spends time with our children,'' said Tom Walsh, the hospital's board chairman.

About 25 children, their parents and hospital officials joined Mrs. Reagan as she listened to traditional Christmas music sung by a choir from Washington-Lee High School in Arlington, Va.

The exchange of gifts began with Mrs. Reagan receiving and then presenting to Walsh a $25,000 check. The donation, a portion of proceeds from NBC-TV's upcoming ''Christmas in Washington'' show, is designated for the renovation of the recreation room that will bear her name. Suzanne Wright, wife of NBC President Robert Wright, gave the first lady the check.

Mrs. Reagan received an artist's rendition of the completed room and visited the facility

''Even though I won't be here touring, I'll be thinking of you and I hope that all children have for all the years to come a very Merry Christmas and the best of health. ... And I'll miss you,'' said Mrs. Reagan in a brief statement.

The first lady gave rag doll to two patients, 5-year-old Terhea Dawkins and 8 1/2 -year-old Marc Amoroso. Marc, who is receiving chemotherapy treatment for leukemia, gave Mrs. Reagan a silk screen print of a horse he did during an earlier hospital stay.

Mrs. Reagan's also delivered gifts to most of the children on the hospital's fourth floor during her two-hour visit. Many of them gave her handmade cards and signs in return.

But the first lady was most moved during her visit with a 13-year-old severely injured girl who had tried to commit suicide.

''I'm happy to meet you,'' said the girl, communicating with Mrs. Reagan in sign language as her father spelled out the words.

''Try to remember that life can be a really wonderful, beautiful, great experience. And it's only given to us once ... so get all you can out of it,'' counseled Mrs. Reagan.

''I understand that now,'' signed the young patient in response.

''Better late than never,'' said the first lady, grasping and rubbing the girl's hand.