I do not recognize the specific fabric but perhaps I can give you some terminolgy to help with your search. The weave itself seems to be a "plain weave", where the yarns cross at 90 degrees. Most fabrics used a consistent size of "yarn" for all the lengthwise (warp) and crosswise (weft) threads. This is often called a "balanced" weave. Another fabric might use one size for all warp and a different size for all weft which is an unbalanced weave, which often makes the fabric have a "rib" texture where the thicker yarns stands above the thinner yarn. Furthermore this tabric seems to use a varying thickness of thick-and-thin yarns in both the weft and the warp. I do not know a specific term for this method or warping. However, Pique fabric, is a type of woven fabric which creates a textured surface such as your example. A common type is "mini waffle fabric" which is close but not an exact match. There are many possible Pique fabrics so one might meet your needs.
Edit: With a little more reseach the same term is used when you vary the distance or spacing between the warp yarns (which is also pften consistent across the width of the fabric) or varying the thickness of warp threads. These changes are called "variable sett" or "varying the sett".