No. There has only been on William, King of Scots. Commonly know as William the Lion. He reigned as King of Scots from 1165 to 1214. His 48-year-long reign was the second longest in Scottish history, and the longest for a Scottish monarch before the Union of the Crowns in 1603. There has been no other William who was King of Scots.

There was a huge outcry in the 1950s here in Scotland when it was announced the late Queen would be know as Queen Elizabeth II. There had never been an Elizabeth as Queen of Scots. When the original cypher EIIR appeared on letter boxes, some were blown up. Eventually the authorities caved and to this day you will only see ER on letter boxes. Police uniforms in Scotland also display ER.

As for what would happen if there was independence in Scotland I seriously doubt it would 'erase' the historic monarchical links of over 300 years. The numeriacy would be hammered out.