Is there any evidence, whether sound or weak, for naming children "Muhammad" or "Ahmad" with an added second name, such as "Muhammad Murshid" or "Jamil Ahmad"?

There is no harm in being named with a compound name of two or more names, or with a single name, as this does not require proof since it is the default, provided that the names do not contain a Sharia-prohibited element. Prohibition is what requires proof, and many Islamic peoples have customarily used compound names, and none of the scholars have objected to that.