Avoiding (or not) the name of deity

So here’s a bit of a puzzlement: The Church of Jesus Christ of Latter-day Saints has a publicly stated position that they don’t want terms like Mormon Church or Church of the Latter-day Saints to be used in publications as short forms of the name of the church, preferring instead that, if a shortened name is needed, The Church of Jesus Christ be used.

Fair enough, i suppose. However, in the scriptural canon (Doctrine & Covenants 107:2–4, if you want to look it up), we’re told that the actual name of what we call the Melchizedek priesthood was actually the holy priesthood, after the order of the son of God—but it was referred to as the Melchizedek priesthood “out of respect or reverence to the name of the Supreme Being, to avoid the too frequent repetition of his name”.

So why isn’t it a problem using names for the church that so frequently repeat the name of a god? And, secondarily, if there’s precedent for replacing references to the name of deity with references to a great individual (e.g., Melchizedek), then whatever in the world is wrong with calling it the Mormon church?