In the name of God vs In God's name

In some pieces of writing it is needed to begin with the name of God; usually centered on top.

Is there any difference between the functionality of "In the name of God" and "In God's name"?

Please, bring suitable (and, if possible, academic) reference.

Thank you all, so much...

Solution 1:

For the desired "Academic reference," scholar.google.com will provide a ranking of the academic books and papers, based on how many other papers cite the given paper.

In the name of God

The search In the name of God yielded about 53,200 results.

In God's name

The search In God's name yielded about 13,900 results.

Papers and books from either alternative deal with religious violence or corruption.

You pays your money and you takes your choice

Without more context, perhaps the OP should guess as to which alternative is more closely aligned with his or her thesis.

Solution 2:

"In the name of God" is more formal (by virtue of its being somewhat old-fashioned) than "In God's name".