I've found this page from an ms of the Notititia Dignitatum which shows shield boss designs supposed to be associated with different 'units' (legions etc.)
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I'm not sure how much certainty we can have about this, ND is a late document (relates to the situation in the western Empire ca 400),
it presents a great many problems of interpretation, and that ms is from the 15th ct, though maybe based on earlier sources. It would make sense for different units to have some distinguishing marks, certainly - though bear in mind, unlike medieval knights, Roman soldiers didn't generally expect to be fighting enemies wearing similar armour and carrying similar shields to their own. Also, the armourers attached to particular units probably had their own distinctive styles. But I'm still doubtful whether there was a regulated system of legionary symbols (on shields, standards or whatever) comparable to modern regimental badges etc., or late medieval heraldry.