There are definitely some "checklist" mnemonics for new climbers, but no standard set. Even among the ACMG & AMGA, every guide and instructor might use something slightly different, or not use any at all.
Here is the one I teach new climbers personally. It's rather simple, but it seems to stick.
Anchor may simply be a check to make sure you are tying in to the correct side of the rope. Belayer is a check to make sure the belay device is rigged correctly (this includes a gate-check for the carabiner), and Climber is a check to make sure the tie-in is done correctly.
In our last guide training day, one of the instructors, a long standing-rock guide, used A.B.C.D.
- Brain-Bucket (helmet)
I've also seen people ad the E to this mnemonic.
- Ends (meaning rope end, which is typically tied with a stopper knot)
The knot prevents the rope from feeding through the device while lowering in the case that you mis-judged the distance of the route.
Another one I've heard in the past is B.A.R.K.
- Buckles (or sometimes brain-bucket)
- Rappel / Belay Device
I've also seen A.B.C.D.H. used as Anchor, Buckles, Carabiner, Device, Helmet, so I'm sure many adaptations exist!
It's important to note that most of these checklists are also very situational so It's somewhat hard to standardize them. I include an additional check for falling ice in winter for example by adding a "D" for dangers, I've also used the "D" for daisy chains in the context of aid climbing. You really do have to pick one that you will remember, and roll with it.
The process of climbing may seem like a lot to remember initially, and does seem to warrant some type of standard checklist, but it sinks in very quick actually because of how much repetition is involved. Additionally, I've found that new climbers are usually very safe and very cautious > the trick is to not get complacent down the line. I've personally caught myself having tied in to only one tie-in point on my harness on more than one occasion.