In Denmark there is only one name that is numbered inconsistently and that name is Waldemar. The first king of Denmark by that name was Waldemar I the Great who was king from 1157-1182. Waldemar II The Victorious, was the son of Waldemar the Great and was king from 1202-1241. There are two individuals that have been labeled Waldemar III. The first is Waldemar the Young son of Waldemar II who was co-king with his father until his death in 1231 but was never sole king in his own right. The other king claiming to be Waldemar III was the son of Duke Eric II of Schleswig and Adelaide of Rendsborg. He was set up as a rival king to the unpopular Christopher II of Denmark 1320-1326. This Waldemar ruled briefly from 1326 to 1329 and again in 1325–26 during the times of upheaval with Christopher II. The son of Christopher II ascended the throne in 1340 as Waldemar IV Atterdag and ruled as a powerful king of Denmark until his death in 1375.
Although not a discrepancy, it is more of an oddity, is the tradition where the kings of Denmark alternated between the names of Christian and Frederik. King Christian I of Denmark, (1448-1481), Norway (1450-1481) and Sweden (1457-1464) was followed by his son Hans (John) of Denmark. John, in turn, was followed by his son, Christian II, until his death in 1523. Christian II was followed by Frederik II and from then on the names of Christian and Frederik alternated until 1972 when it was interrupted with the accession of Denmark’s present queen, Margrethe II. This tradition will carry on for a while it seems after Margrethe when her son, Crown Prince Frederik, eventually succeeds as King Frederik X and when his son eventually succeeds as King Christian XI. After the reign of Christian XI, far in the future, it remains to be seen how this tradition will be continued given the fact that absolute Absolute cognatic primogeniture was adopted in 2009. Absolute cognatic primogeniture is where titles and inheritance is passed to the eldest child regardless of gender.