In Shropshire Isla and Harry have become the new most popular baby names, while in Telford & Wrekin it was Isabella and Oliver.
In Powys it was George or Oliver for boys, and Olivia for girls.
Office for National Statistics (ONS) figures show 24 newborns in Shropshire were given the name Isla last year – though this was two fewer than the previous year's top ranked Olivia. Meanwhile, 31 boys were called Harry in 2019 – 10 fewer than former top spot Arthur the year before.
In Telford,19 newborns were named Isabella last year, some four fewer than the 2018 favourite, Olivia. Meanwhile, 22 boys were called Oliver – three more than Archie the year before.
In Powys, 12 newborns were given the name George or Oliver and 11 babies were named Olivia.
Nationally, Oliver remained the most popular name for boys in England and Wales for the seventh year in a row, ahead of George and Noah.
Olivia topped the girls' list for the fourth year in succession, with Amelia and Isla in second and third respectively.
There were no new entries in the top 10 boys' names, though the ONS noted a few trends which were possibly being influenced by popular culture.
The number of boys named Kylo has risen from just 10 to 67 between 2015 and 2019, a period of time which saw the release of a new Star Wars trilogy, featuring the leading character of Kylo Ren.
Taron Egerton, star of the 2019 award-winning Elton John biopic Rocketman, may have been why 48 boys were given that name in 2019 – the most since detailed records began in 1996.
Freya entered the top 10 girls' names for the first time, while Mabel returned to the top 100 for the first time since 1924.
But some previously popular names were almost completely absent, with just two or fewer baby girls named Brittany or Kerry last year.
David Corps, from the ONS, said: "Oliver and Olivia continued their reign as the top boys' and girls' names in 2019, but analysis shows choices in baby names can differ depending on the mother’s age.
"We found younger mothers opted for more modern girls' names like Harper, which has seen a rise since the Beckhams named their daughter so in 2011, and shortened boys' names like Freddie. In contrast, older mothers chose more traditional names such as Jack and Charlotte.
“Popular culture continues to influence the baby names landscape. Following Dua Lipa’s first UK number one single in 2017, the number of girls named Dua has doubled from 63 to 126 in 2019.”