Glenn said:
Then it would be either ディルドラ or ディアドラ, I believe.
Not ディルドラ I think. It's probably not a short vowel for a start and (more importantly) stick the word in WWWJDIC.
ディールドラ wouldn't be impossible.
Leaving pronunciation to one side for the moment,
spelling and
expectation are two other relevant points. Will people seeing your name in katakana be able to work out what it was in English and how common is your katakana name? These factors affect how likely it is you will be told your name is 'spelt wrong'.
ディードル 217 ディードル + deirdre 22
ディールドレ 2 ディールドレ + deirdre 2
ディアドゥリ 19 ディアドゥリ + deirdre 4
ディアドリー 163 ディアドリー + deirdre 31
ディルドラ 6 ディルドラ + deirdre 0 ← Seriously, don't get this one.
ディールドラ 4 ディールドラ + deirdre 0 ← Or this one by the look of it.
ディアドラ 13900* ディアドラ + deirdre 144
*
NOTE Diadora is some sort of computer company. Nearly all those hits will be for Diadora.