Do you have a budget range in mind? A measured plan of the backyard indicating north, south etc. would be helpful.

I take it we're looking at the back of the back yard neighbor's house? The picture is not enough for us to understand your back yard. Give us an entire panorama that includes your house for a point of reference. Easiest to do by taking slightly overlapping shots -- a 180* view -- while you stand in ONE spot, at the back, center of your house and pivot with the camera. Start the series of pictures looking left and including the wall of your house. Finish by looking right and including the wall of your house. Please take when light is good.

Do any trees grow there? Do you know what kind?

Yes, looking at neighbor's house. Ok on photo. It is a new build, not moved in yet, so I'll try a panorama shot next time I visit. I think El Paso is Zone 9. For trees I'm considering Desert Willow, Goldenball Lead tree, Flameleaf Sumac, Mexican Plum, TX Mt. Laurel, Mexican Buckeye, Chinese Pistache, and Lacebark Elm.

It is a good looking wall. If you strategically place trees, you might not need an additional panel. Don't plant the trees too close to the wall, but closer to where you need some privacy. Shade trees are very helpful in enjoying the out of doors.

Most of the trees you mentions seem to be shrubs or very small trees. The Mexican Plum gets to be 25 tall, so that one would be a good candidate. The Mexican Buckeye looks like it is very attractive plant. The Texas Mountain Laurel is very attractive.

Texas Mountain Laurel - Mescal Bean Sophora · More Info

Here is a privacy screen from a firm in Dallas.

Privacy Screening · More Info

Privacy Screening · More Info

Clumping bamboos make excellent specimen plants and will form very dense screens when planted in a line. We believe these types are most suitable for suburban yards and gardens and landscape much like a medium sized tree.

They have a short horizontal root structure, are genetically incapable of expanding more than a few inches a year and will generally form discrete clumps. The clumps slowly enlarge as new culms emerge every year [and may require anywhere from 8-10 feet in diameter for their planting area].

----There are two main types of bamboo: running and clumping. Running bamboos spread with cable-like rhizomes. Bamboo Texas specializes in CLUMPING bamboo that will not spread and take over your yard (or your neighbor's).

https://www.bambootexas.com/about-bamboo/

Kathleen Shaeffer Design, Exterior Spaces: "It's Bambusa oldhamii, a clumping timber bamboo."

Santa Cruz III · More Info

Is the top of the wall flat -- will it hold rectangle pots with plants that will hang downward that will grow in your planting zone? That could hide/soften the look parts of your wall.

https://parkseed.com/silver-falls-dichondra-ground-cover-seeds/p/03235/?gclid=EAIaIQobChMIorP0s4ay6gIVS7LICh1MbQtOEAYYBCABEgKVmPD_BwE&utm_source=google&utm_medium=cpc&utm_campaign=ppc_google_pla&ef_id=EAIaIQobChMIorP0s4ay6gIVS7LICh1MbQtOEAYYBCABEgKVmPD_BwE:G:s

https://www.irwinstone.com/how-tos/build-stone-wall/ 

Consider creating a walk path around the perimeter a couple feet from the wall and planting between it and the wall except for trees you might want in the center farther from any foundation of house or wall.

Could you alter the top of the wall by adding 3" thick concrete cap blocks and/or or building a form and add one rectangle of concrete to it at a time over time?.

https://www.poolweb.com/steel-spring-clamps-for-wall-cap-forms-case-of-10-clamps?gclid=EAIaIQobChMI8IWutIWy6gIVuey1Ch26OgdMEAYYBCABEgLHj_D_BwE

With plenty of sun, adding a plain concrete bird bath with a solar water pump is worth considering. Back yard bird watching can be entertaining.

Consider balancing what you plant -- two of each -- especially anything that blooms ... think pollination: choose some flowering plants that add color and attract butterflies.

Pay attention to the path of the sun -- A couple of carefully placed tall broad leaf trees that lose their leaves in winter will give you summer shade and winter sunlight/warmth and have a positive impact on your heat/ac bill.

Think symmetrical planting. Consider creating a mulching space between that back far wall and the plants you put nearest it for privacy -- shrubs that could hide the mulch space, too.

Pick at least two shrubs or trees that keep their leaves year round -- green in your back yard year round will make it more inviting.

https://txmg.org/elpaso/learn/gardening-in-el-paso-articles/fruit-trees-for-el-paso/ 

Consider planting a food producing plant ... even if it is strawberries in baskets hung on posts.

Appears to be a subdivision so likely has a connection to the public water/sewage system?

Save on watering costs: Building regs permitting, if you can direct your laundry drain and/or a kitchen sink drain toward watering them, you're plants might appreciate it.

https://www.etsy.com/listing/778942398/laundry-to-landscape-greywater-kit?gpla=1&gao=1&;

"Month by month gardening for Texas"

https://txmg.org/elpaso/learn/gardening-in-el-paso-articles/fruit-trees-for-el-paso/.

Excellent info. suezbell! Top of wall is not flat. All the other info. you provided will be seriously considered and most likely incorporated in my design. Thank you.

Budget is HIGHLY ECONOMICAL one or in commoner terms: CHEAP. And no time frame to complete.

Hi, IMO Mountain Lauren is a beautiful tree - I have a couple of them. However, the pods with the red berries that drop drive me nuts because they can sprout easily.

I note the porch roof. What is the shape -- length/width of the back yard.

The new pictures help. (No time now, though, to do any anything with.) The fence panel that has been added to top of wall, it that by neighbor? And will you want to continue that treatment?

Some ideas

This is generic and organizational, not about specific plants. Not knowing the general direction you want to take with plants, Iook more at plant heights than what a plant might tend to resemble. For instance, what looks like grass might be gravel if you're going hard xeriscape. It could also be fake grass (but that's not cheap.) The small tree made out of a large shrub would be useful to you for screening neighboring properties. You might want to expand the patio in the future.

Nice Yardvaark. A lot of what you provided is right with what I was thinking. Patio expansion was considered. Paneling is neighbor's. Not decided on continuing.

Suezbell Yard is rectangle, probably 35 x 56 ft.