Yes, many do, or can. Some funeral homes historically were in the "marker" business generations ago, but currently, its more likely than not, that they are separate enterprises, but you would be correct in your thinking that funeral homes are a logical place to bring your inquiries. Many funeral homes act as Independent Contractors to execute the sale through a local monument company whereby the funeral home may either be paid a commission on the sale, or simply monitor the sale at no cost for the benefit of their clients. Some funeral homes may choose not to become involved in the sale at all, but most certainly can direct their clients to reputable artisans. Keep in mind, the material, shape and size of your particular maker or monument may be regulated by the cemetery. Many "memorial parks" may only allow "flush" markers in all or certain sections of the cemetery. Other cemeteries may contain regulations on size or even standardize what they believe is appropriate in wording or symbolic appearance of the markers. Also, be mindful, marker pricing, like any other purchase, can vary widely. And, not only must one be concerned with the price of the marker, but there may well be an installation, setting, lettering, foundation, and permit fees to be concerned with, and state tax.
