Here's a story of a recent monogram showing the evolution from start to finish.

Even a "simple-looking" monogram has hidden complexities.
Once upon a time, a client asked me to design a business logo (for an art-consultant business) based on the monogram of the last Tsar and Tsarina of Russia, Nicholas and Alexandra.

You see the imperial monogram above. Reflected double AA atop eachother and intervoven with a cyrillic N (which looks like an H to our eyes).

Using a double A and a latin N this time I came up with the following compositions.
As often happens, I rush forward with my favorite design and come up with a more completed refined version seen above.
(Of course this un-contracted work is not "on the clock".)

I sent these sketches to the client and he felt the one I preferred was lovely but too lyrical.

He chose the composition below:
He also mentioned that he wanted it to be finished in two solid colors, no crosshatching or other detailing needed.

Having refined it further I came up with the following variants on a theme:
Most of the above show the numerous ways the few lines of the monogram can be intertwined
I composed a "letter" and placed the one he perferred at the top to show him how it might look in situ.

FYI: "caca-dauphin" is a true color name quite in fashion with the elite of the 18th century. It roughly translates as "royal baby-shit brown." It seems to me that that hue would be a downgrade from aubergine, but color is not my strong suit.
The client was 90 percent happy, but wanted the trapezoid of the AA to be wider.

I sent off the options shown above, some of which involved widening the N as well as not to cause tight areas from being too overly congested.

The client made his choice and I interwove the monogram and the resulting final version is shown below.
Were this in color you would see the N printed in a beautiful shade of aubergine hoarmonzing perfectly with the double A printed in puce accented with a slight hint of caca-dauphin.