Is their a fallacy for when someone synomymize one subject for another?

I don't think that defining God as the universe is a useless definition. Someone could change their behavior by acknowledging this. For example, there are some people that respect nature because they believe that it is their God. I don't know what you mean by a "deceptive way to sidestep or shift the burden of proof as their God is a proven assertion." Do you mean proof for the divine? If so, then I agree. Saying that nature has divinity because we can see it presupposes that divinity can be seen. But for 'X is the same as Y. Since Y exists, this proves X exists' and "an example is when someone defines their God as everything in existence" does not commit a fallacy at it. This would be the same thing as saying that "my God is science. I can see science. Therefore my God exists." If you're worried about implications about the spiritual world, simply ask if that's what they mean.

Well, it very much depends on the definition of that tiny word "is".

If "is" is used to state material equivalence, the statement is true. As in:

Even numbers are the same as (are equivalent to) numbers divisible by 2
Numbers divisible by 2 exist,
Therefore even numbers exist.

(let's leave the question of the 0 out for the moment...)

If "is" stands for implication, it is false. For example:

A squares is (implies) a rectangle.
Rectangles exist.
???

this is not sufficient proof that squares exits, in fact there's a fallacy for trying to make such a deduction (Affirming the consequent<>).

The question is now whether the thing that someone compares "God" with is a material equivalence or a an implication.

Well, if, for example, you have a statement like "God is goodness and goodness exists", then God certainly isn't a material equivalent (that would be such a narrow definition of "God" that even most Atheists could sign up to it), but rather somebody stating his or her definition of God implies goodness. Nothing wrong with that per se. But deducting from it the existence of God is certainly is commiting the affirming the consequent-fallacy.

When thinking about what could possibly be counted as a material equivalence, the best I could find is The Holy Spirit (spiritus sanctus), which by some rather suspicious catholic doctrine is supposedly both equivalent to God and a part of it/him. There are probably some other logical problems with this, but let's assume the first premise to be:

God is the same as The Holy Spirit.

That's a lot better, but now we have to problem how to prove the existence of The Holy Spirit. So effectively we just shifted the problem from one term to another...

So in the end, affirming the consequent is probably our best bet in any case.

{u}Edit:{/u} On second thought: it might be a nice challenge to make a case for material equivalence of "God" and "Jesus" and try to deduct the existence of God without falling for the Fallacy of Equivalence. Anyone up for the challenge? ;-9