They already are. And that includes us humans. You just can't see it.
Our patterns are called Blaschko's lines. They exist because when we are embryos, the cells that will form our skin migrate in waves to where they will be. In almost every human the cells are all genetically identical, but if some of the first cells mutate, or in the case of chimeric people, there will be different populations of cells in the skin.
In such cases, should a condition affect only one population of the cells or affect each population differently, the patterns may become visible. They look like this:
Notice that this is not the same as vitiligo.
It is also possible for someone to have two skin cell lineages and have no visible patterns - under visible light. Sometimes these patterns are only visible in UV. You can try and find out if you are chimeric by exposing yourself to a UV lamp (the odds are pretty low).
If you wish for hominids in your world to have such patterns without the need for mutations or chimerism, have the skin pigmentation genes to activate just like most genes in the X chromossome do. In every cis woman's cells, one of the X chromossomes is shut down. The one that is shut is decided at random early during embryo stages, so there are whole patches of skin cells grouped together with only her mother's or her father's X chromossome activated.
If you want both sexes to display this characteristic, either have the genes for it outside the X chromossome, or have them in the X and also in the combining regions of the Y.
Last but not least, remember that just as genes can affect skin as described above, they can also affect hair and fur. So you can decide whether you wish for the patterns to exist only for the skin, for the coat, or for both.