What exactly do you mean by personalize? If you mean were they able to pesonally determine their appearence, the answer is “sort of.” By Late Antiquity, the production of military equipment was largely centralized in state-run arsenals known as fabricae. Prior to their creation, it appears the army was supplied by a system of private contractors (though I cannot comment too much on this system as it’s something I have not studied in detail). Military equipment like swords, body armor, and helmets thus would have largely been standard throughout the Empire and, as it was issued by the state, individual soldiers would probably have had little say in what equipment they were issued.

That said, there was always a degree of “local flavor” in military equipment, especially in the clothing worn under armor. This would have been especially true for a unit on campaign, when clothing (which deteriorates surprisingly quickly in the field) would have been acquired from local sources. “Uniforms” in the modern sense of the word did not exist in the Roman world, and soldiers had latitude in determining aspects of their dress, especially the woven patches (orbiculii and clavii) that decorated military tunics during Late Antiquity, though it appears that various shades of undyed wool were the dominant colors (though this is debated, and soldiers could and did wear tunics of more vibrant colors). A unit of Roman soldiers would therefore have been relatively uniform in appearance, but this appearance would have varied across the Empire.