The thing is: this is a name than gets pronounced both ways. Listen for example to http://www.forvo.com/word/perdita/
What did Shakespeare intend? Hard to be sure. Sometimes, a name in Shakespeare appears in a formal verse form, such that one can tell where he intended the stress to lie. Not so here. Although, there are these lines from Paulina:
That she is living,
Were it but told you, should be hooted at
Like an old tale: but it appears she lives,
Though yet she speak not. Mark a little while.
Please you to interpose, fair madam: kneel
And pray your mother’s blessing. Turn, good lady;
Our Perdita is found.
Which to my ear sound as if the name sits more happily with the stress on the first syllable. And this is how it is usually pronounced in classical productions. Albeit that Yahoo Answers is the other way around.
Neither is it clear what Dodie Smith would have had in mind. But by the time 101 Dalmations the big screen with Disney, is was PerDEETa, with the stress on the second syllable. Not that we care much how other people pronounce the name.
For the time being, she is PerDEEta, because she is still the deeter dog. When she grows up, and becomes better behaved, she might grow into a PERdita. We shall see.