Phyla nodiflora, aka Lippia, and aka Kurapia if of the Japanese bred lineage.

(Click on underlined blog entry title to see more) Possibly native to the California Floristic Province, and(or), possibly not.  Calflora lists it as native to Calflora.   That matter is uncertain by the most prominent botanists, but South America is consistently figured the most likely 'home region', though it's figured native to other regions, including North America, at least by some official state level botanical references.  This example of Phyla being grown as turf, is growing in a front yard lawn space in Point Loma, north facing lawn.   Phyla nodiflora, makes a durable interesting lawn-turf, with lower water needs than other grass lawns, hardy enough for some modest walking and playing use without much damage, and it quickly re-grows if damaged.  This particular 'strain' was taken from the wild near Lake Henshaw, in the northeast part of San Diego County.   The species is native from California through to the west coast of South America.   It's not common, first of all, and not very noticeable in the wild, since it's very low growing, besides it's uncommonness.   And even besides those factors, it's a rather durable plant.   Does well in full sun to half day sun or at least bright light.  It's a fast growing 'running' groundcover, which stays low like hybrid bermuda, though requires less water than even Bermuda grass lawns to keep reasonably green. and basically no mowing as long as it's not watered too much.   Has pretty 'verbena-like' small flowers spring through summer.  It can attract bees, but usually not much, if that's a concern.  If you absolutely want no likely chance of bees  on the turf, then use a grass lawn, if you want turf space.  Top photo is in late summer, bottom up-close photo is in spring.   Btw, there's a Japanese-bred lineage of Phyla nodiflora called 'Kurapia' which is apparently even more drought tolerant than the standard Phyla nodiflora, which is moderately/fairly drought tolerant, with good performance occurring under such conditions.

CSLB
C27 893456

ISA
WE-8027A

Green Thumb San Diego Comprehensive Landscape Design Plants