When a garment carries both your organisation logo and an employee’s name, the two are best planned as one visual system rather than as two separate embroidery decisions.
The common arrangement is the organisation logo at left chest with the employee name, and a role where you want one, at right chest. That is a common approach rather than a universal rule — pockets, seams, zips, garment style, the shape of your logo, how long staff names run, whether role information is included and any other branding you need can all point somewhere else.