Wales/Welsh isn't Gaelic.
The Celtic groups are:
- Scotland
- Ireland
- Wales
- Cornwall
- Isle of Man
- Brittany (in France)
The languages are sub-divided:
Irish, Scottish Gaelic and Manx are Goidelic (Gaelic).
Welsh, Breton and Cornish are Brythonic.
It's probably much easier to think of looking for a Celtic name rather than a Gaelic name, or a specifically Irish or Scottish name if going for a particular region.
So, for example (I'll stick with the three most known Celtic regions):
Welsh names: Arwen, Gwendolyn, Rhiannon, Carys, etc.
Irish names: Shauna, Shannon, Sinead, etc.
Scottish names: Bonnie, Kyla, Maisie, Vanora, etc.