Edit your addons/adminmod/config/adminmod.cfg in file manager and look for:
// The old verbosity. Defines how commands are announced to the players
// clients in the form: "[ADMIN] <user> used command <command>"
// 0=all commands announced in chat with the admin name
// 1=all commands announced in chat, but without the admin name
// 2=most commands not announced at all (except "cheat" commands)
Change admin_quiet to 2