Info: Kamen Rider Solomon's Sword Name & Emotional Dragon's Black & White Dragon's Name
Master Logos / Kamen Rider Solomon's Repainted King Excalibur is called as "Caladbolg".
This is the correct way of writing it. But I am pretty sure that Toei will butcher it when romanizing.
As per Wikipedia,
Caladbolg ("hard cleft", cognate with Middle Welsh: Caledfwlch in medieval Welsh literature and Excalibur in the Matter of Britain; the name appears in the plural as a generic word for "great swords" in the 10th-century Irish translation of the classical tale The Destruction of Troy, Togail Troí), sometimes written Caladcholg ("hard blade"), is the sword of Fergus mac Róich from the Ulster Cycle of Irish mythology. Spelled Caladcholg, it is also associated with the more obscure Ulster hero Fergus mac Léti, suggesting a conflation of two legends. It was said to be a two-handed sword that made a circle like an arc of rainbow when swung, and to have the power to slice the tops off hills and slaughter an entire army.
The Black & White Dragons in Emotional Dragon have their own names. Black Dragon is called Rune Dim Dragon & the White Dragon is called Rune Bright Dragon.