In the interest of accuracy, and not meaning to bore anyone to death, I have encountered additional information of the Morados Viejos from Spanish sources that would indicate that it did not become the Regiment de Sevilla as I previously indicated.
In fact, I found a wonderful regimental history from a Spanish source that traces the unit from its origins under Philip IV in 1632 (although not sanctioned by Royal decree until September 10, 1634) until far beyond our time period, in the later 18th century.
According to this history, which is well annotated and appears well-supported, the Morados Viejos became instead the Regiment de Castilla in 1707 due to their association with the Kings of Castille, their seniority, and their use by Philip V as the "core" unit in his new infantry organization. In fact, later in their history, their name was changed several times and included "The King's Regiment of Castille" and "The 1st, or Immemorial Regiment of the King". Even later it is referred to officially as the "1st Regiment of Foot, The King's Regiment"
Much like the Regiment de Picardie in France and the 1st Regiment of Foot, the Royal Scots, in England, this regiment holds official "pride of place" as the "birthplace of the Ancient Spanish Army" in writings attributed directly to King Carlos III in the mid-18th century.
I would highly recommend that anyone wishing to further research the various Infantry Regiments of Spain peruse the following web site (I have provided a link to the Google translation) and follow the links to specific unit histories. Very well done effort. http://18.104.22.168/translate_c?hl=en&sl=es&u=http://www.geocities.com/Pentagon/8745/infanteria/1704-09.htm&prev=/search%3Fq%3Dhttp://www.geocities.com/Pentagon/8745/infanteria/historia.htm%26hl%3Den%26sa%3DG&rurl=translate.google.com&usg=ALkJrhh2GHGH98xmAd6D9yWGLa5PJsxdLw