The question was about a possible use of soon-to-be Saint John Paul’s name in the litany of saints. There are several “official” versions, including the stand-alone litany, which is one of only four litanies approved for public use. There is also the version used at the Easter Vigil (slightly different in its EF and OF versions), a shorter one used at baptism and confirmation, and another short form that can be used as part of the funeral rites. There is no guarantee that his name would specifically be listed in any of these, but there are options in the shorter forms to insert saints of one’s choosing, so certainly it could be used there.
Which form of a canonized pope’s name is used depends on the context. When speaking and generally referring to them, they are referred to by their names, such as St. Piux V, St. Pius X, etc. In this context, it would be St. John Paul II. When popes as a group, whether canonized or not, are being listed, and various popes being referred to in their capacity as supreme pontiffs, then it is common to see them referred to as Pope St. Pius X, Blessed Pius IX, etc. But in prayers and the litany, no numerals are used, and no soubriquets such as “the Great.” St. Gregory the Great is not called that in his Mass or in the litany, just St. Gregory.