MTGNexus

Ludevic, Necro-Alchemist is one my partner commanders and out on the battlefield. I also control Loyal Subordinate and say 8 random creature tokens. During my pre-combat main phase I use Mirrorweave to make every creature a copy of Loyal Subordinate.

When it goes to my combat, even though my commander is turned into a different creature, will all 10 of my Loyal Subordinates (including the former Ludevic) still see I control a commander and trigger to make my opponents each lose 30 life? In other words turning my commander into something else doesn't stop it from being my commander, right?

Right. Commander...ness is a value of a literal, physical card. Being a commander, is, as MTGCommander.net's rules say, "a property of the card and not a characteristic of the game object."

903.3.
Each deck has a legendary creature card designated as its commander. This designation is not a characteristic of the object represented by the card; rather, it is an attribute of the card itself. The card retains this designation even when it changes zones.
Example: A commander that's been turned face down (due to Ixidron's effect, for example) is still a commander. A commander that's copying another card (due to Cytoshape's effect, for example) is still a commander. A permanent that's copying a commander (such as a Body Double, for example, copying a commander in a player's graveyard) is not a commander.

From my understanding the commander type is attached to the physical card. It doesn't matter if you copy another creature, it's morphed, flipped, coloured green or ten inches big.
So yes, it's still your commander.