The practice of referring to a regiment by the name of its colonel was pretty common in the Trans-Mississippi Army. You almost never see that done in the Army of Northern Virginia or Army of Tennessee.

However, all Confederate armies followed that practice in the case of artillery batteries. Most artillery batteries had a high-falutin' name, like the "Confederate Guards Artillery" or "Salem Flying Artillery", but with few exceptions these names were never used. Instead, the battery was identified with the name of its current captain.

Likewise with brigades, divisions and, to a lesser extent, corps. Most armies assigned numerical designations to these organizations, but they were rarely used. Like artillery batteries, they were usually identified with the name of their respective commanders, e.g., Rust's Brigade, Fagan's Division, Longstreet's Corps, etc.