You have many options: Callicarpa americana, Mexican plum, rhus aromatic. holly, Mexican buckhorn, Mountain Laurel, Rough leaf dogwoog (among many others). Here you have more from Pinterest

Omar

I'd plant several different varieties of evergreen shrubs such as those suggested by Omar and by others who will be making suggestions here. It makes for a much more interesting landscape and you will not have a "wall effect" you mentioned not wanting. Plus if one dies you can replace it without it being so obvious.

7ft+ hedges were used a lot in our part of Dallas where the rear entrance alleys run adjacent to major boulevards. Seems to be a palette of 4 to 6 evergreen shrubs that work well here in sun, so hedge type often varies by the lot rather than a couple blocks of the same. Looks much nicer than the protective barriers they often hide, but agree with the earlier posts on liking greater variation better.

Dwarf wax myrtle and yaupon holly are two good natives that will work in shade; 'Scarlet's Peak' is newer narrow female cultivar of yaupon. I've heard Agarita can take some shade, but is uncommon here and have not seen this done in person. Anyone know?

Two flowering non-native evergreens that grow reasonably fast and work well in partial shade include standard Abelia and Loropetalum. Aucuba and Leatherleaf Mahonia can take heavier shade. Our boxwood hedge actually does very well with the winter sun and heavy summer shade of its deciduous canopy. Standard Nandina has also been used well (and poorly) around here in shade for years. All of these are capable of growing over 6ft tall, but can take many years for some - especially in low light locations.

Cleyera and some Camellia cultivars can work in partial north Texas shade, but usually have to prep/maintain soil to be a bit more acidic than the alkaline clay common to the area to avoid chlorosis problems.