Changing your name by deed poll in Wales works in exactly the same way as in England. Wales shares the same legal system as England under English and Welsh law, so a deed poll executed in Wales is identical in legal effect to one executed in England. The Passport Office, DVLA, banks, HMRC, and your GP all accept deed polls from Welsh residents without any difference in process or requirements.
For Welsh speakers, there is a practical question about language. A deed poll can be drafted in Welsh, in English, or bilingually. Most organisations in Wales are legally required under the Welsh Language Act 1993 and Welsh Language (Wales) Measure 2011 to accept documents and conduct business in Welsh. If you wish to have your deed poll in Welsh or in a bilingual format, this is legally valid and is your right. However, organisations outside Wales that operate only in English may have difficulty processing a Welsh-only deed poll; a bilingual version (Welsh and English) is usually the more practical choice if you anticipate presenting it to organisations throughout the UK.
The deed poll this service generates is in English, which is accepted across the whole of the UK without issue. If you specifically require a bilingual Welsh-English deed poll, a solicitor in Wales experienced in Welsh language legal documents can assist with this. For most people, an English deed poll is the simplest and most universally accepted option even in Wales.