For the most part I expect that they are primarily identified by darker skin color and perhaps to some extent facial features. These factors are more or less prominent in different individuals. For example, see the photographs accompanying ‘They won’t accept us’: Roma refugees forced to camp at Prague train station at theguardian.com.
I can also relate a story about appearance based anti-Roma discrimination. I once went to a swimming pool operated by a private company in a central European city that has a small but visible Roma population. I was in a group that included an Indian man. He was initially refused admittance, but when the person at the door found out that he was from India, he was allowed in.
I don't have much knowledge of Romani names, but I suspect that this is also a way of identifying Romani people. The man profiled in the Guardian article has what must be a common Ukrainian name as it means "George," but his surname, Stan, does not seem to be Slavic nor German.
I have seen quite a lot of distinctive traditional Romani clothing, primarily at cultural festivals and performances. An internet image search for "roma refugees ukraine" showed such clothing in only one image, which was a photograph of a dance performance in a refugee camp, so I doubt that this is a useful means of discrimination.
According to Change in approach aims to deter Roma refugees from english.radio.cz, the Czech government is discriminating against Roma refugees indirectly by virtue of the fact that many Ukrainian Roma possess Hungarian nationality. In this case, the identifying factor is the possession of a passport from an EU country.
(In fact, this is a legitimate ground for excluding someone from refugee status under international law, but it also means that they cannot be forcibly expelled from the country without reason, and despite the minister's baffling suggestion that they should return to Ukraine, if they were to be expelled, they should be sent to Hungary or whatever other EU country whose citizenship they hold.)