Plenty of healthcare uniforms carry two pieces of information: who the organisation is, and who the person wearing it is. Treated separately they tend to look like two decisions. Treated together they look deliberate.
A common arrangement is the organisation logo at left chest with the employee name, and sometimes a role, at right chest. That is a common approach rather than a universal rule — pockets, garment style, logo shape, how long staff names run, whether role information is included and any other required branding can all point to a different arrangement.