普通の(素の)DatePicker
は、何もしなくても日本語になると思います。
xml
1<Window
2 x:Class="Qs88bt90k25ufz4.MainWindow"
3 xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
4 xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
5 Width="800"
6 Height="450">
7 <StackPanel>
8 <DatePicker />
9 </StackPanel>
10</Window>

画像を見る限り「Material Design In XAML Toolkit」のようですね。
不具合があったようですけど、今は直ってそうですよ。
Informations in the DatePicker are half-translated · Issue #2318 · MaterialDesignInXAML/MaterialDesignInXamlToolkit
.NET 6.0
NuGet Gallery | MaterialDesignThemes 4.5.0
xml
1<Window
2 x:Class="Qs88bt90k25ufz4.MainWindow"
3 xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
4 xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
5 Width="800"
6 Height="450">
7 <StackPanel>
8 <DatePicker Language="ja" />
9 </StackPanel>
10</Window>
xml
1<Application
2 x:Class="Qs88bt90k25ufz4.App"
3 xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
4 xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
5 xmlns:materialDesign="http://materialdesigninxaml.net/winfx/xaml/themes"
6 StartupUri="MainWindow.xaml">
7 <Application.Resources>
8 <ResourceDictionary>
9 <ResourceDictionary.MergedDictionaries>
10 <materialDesign:BundledTheme
11 BaseTheme="Light"
12 PrimaryColor="DeepPurple"
13 SecondaryColor="Lime" />
14 <ResourceDictionary Source="pack://application:,,,/MaterialDesignThemes.Wpf;component/Themes/MaterialDesignTheme.Defaults.xaml" />
15 </ResourceDictionary.MergedDictionaries>
16 </ResourceDictionary>
17 </Application.Resources>
18</Application>
