Whose glory are we talking about?

In the mass as official, I find:

Priest:  Pray, my brothers and sisters, that our sacrifice
may be acceptable to God, the almighty Father.
All:  May the Lord accept the sacrifice at your hands,
for the praise and glory of his name,
for our good, and the good of all his Church.

It’s just before the preface, followed by holy, holy, etc., the old “Orate Fratres.”   Fine.

But I hear oftener and oftener this:

Priest:  Pray, my brothers and sisters, that our sacrifice
may be acceptable to God, the almighty Father.
All:  May the Lord accept the sacrifice at your hands,
for the praise and glory of God’s name,
for our good, and the good of all his Church.

Why do priests do that?  Remove the “his” for the unnecessary “God’s”?  Whose else would it be?  I suspect it’s a sort of between-us-chickens thing: “his” is masculine, and there’s too much of that in the church.  So start saying “God’s,” and people will get the message.

Look, if that’s why they do it, why don’t they preach on the topic?  Tell parishioners who pay attention what they are doing and why?

Later: Another oddity, heard just yesterday,

He has come to the help of his servant Israel
for he remembered his promise of mercy,
the promise he made to our fathers,
to Abraham and his children for ever.”

in the Luke passage becomes

He has come to the help of his servant Israel
for he remembered his promise of mercy,
the promise he made to our ancestors,
to Abraham and his children for ever.”

No faceless bureaucrat is doing this, but the priest on the spot.  Somewhere they are picking this up, but they are not telling us where.