。
Please write your name on all your belongings.
Literal
Belongings all [on-に] write-name do-[て]-please.
Instructional register, typical of school or lost-property notices. 記名する = 'to write one's name (on X),' a formal Sino-Japanese compound verb. 持ち物 = 'belongings, things one carries' (from 持つ 'to hold/carry' + 物 'thing'). The に here marks the location/target of the name-writing.