It was spelled Cadwallader in Shakespeare's "Henry V," though most likely pronounced as Cadwalader would be. Then again poor Captain Llewelyn (which was likely his real name) was called Fluellen the whole time...
Someone said they prefer the spelling Cadwallader. This would be pronounced wrong if said with an 'l' sound.To say Cadwallader, the 'll' is pronounced by putting your tongue to say 'l' then blowing out. (and don't forget that all the other letters are 'hard', not 'soft) Hope I've cleared this up for folks!
I certainly did not mean to suggest that there is anything wrong with using the variant "Cadwallader," though it would indicate an incorrect pronunciation in Welsh. Names undergo mutations all the time and always have.
You might think it looks nicer with two ll's, but this would indicate an incorrect pronunciation. (The double l in Welsh is voiceless, unlike the single l in Cadwalader.)