what's the difference 'wo' and 'wa'?
Boku no namae wa Dezmond desu.
this means my name is Dezmond.

I've also seen it used like "Kanojo no namae wo Ashley desu."
Her name is Ashley.

Is it just slang, is it just the same word but for different meaning (like how you can say "dewanai" or "dewaarimasen" but they basically mean the same thing) or ?

Question

what's the difference 'wo' and 'wa'?
Boku no namae wa Dezmond desu.
>>this means my name is Dezmond.

I've also seen it used like "Kanojo no namae wo Ashley desu."
>>Her name is Ashley.

Is it just slang, is it just the same word but for different meaning (like how you can say "dewanai" or "dewaarimasen" but they basically mean the same thing) or ?

Answer

I'm not Japanese, but I have done a lot of studying of Japanese particles and I have to say that using "wo" in this context is completely wrong. This is because "wo" and "wa" have totally different grammatical functions: "wo" is used to mark the direct object of a sentence, whereas "wa" is used as a topic marker, in other words to alert the listener that some key information is just around the corner.

Answer

dewanai you can used in informal moments
dewaarimassem you can used in formal moments

Answer

"Kanojo no namae wo Ashley desu." is dead wrong. 

There's only a handful of situations where you could use 'wo' like that. For example: 

"Uragiri wa boku no namae wo shitte iru." -> Betrayal knows my name. 

Naturally, 'wo' is still an object marker there.

Answer

It is wrong. 
× "Kanojo no namae wo Ashley desu."
○ "Kanojo no namae wa Ashley desu."