Hi,
please change your XAML:
<Window x:Class="MultiTextBoxName.MainWindow"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:materialdesign="http://materialdesigninxaml.net/winfx/xaml/themes"
xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
mc:Ignorable="d"
Title="MainWindow" Height="450" Width="800">
<Window.Resources>
<ControlTemplate x:Key="MultiTextBoxTemplate" TargetType="ContentControl">
<Grid FlowDirection="LeftToRight">
<Grid.ColumnDefinitions>
<ColumnDefinition Width="*"/>
<ColumnDefinition Width="*"/>
<ColumnDefinition Width="*"/>
</Grid.ColumnDefinitions>
<TextBox x:Name="dummyTextBox" Grid.Column="0" TextAlignment="Left" HorizontalAlignment="Stretch" Grid.ColumnSpan="3"
materialdesign:HintAssist.Hint="{Binding Path=(materialdesign:HintAssist.Hint),RelativeSource={RelativeSource Mode=TemplatedParent}}"
materialdesign:HintAssist.IsFloating="False"
materialdesign:HintAssist.HintOpacity="0.10"
materialdesign:HintAssist.FloatingHintHorizontalAlignment="Right"
Style="{DynamicResource MaterialDesignFloatingHintTextBox}"
IsTabStop="False" IsHitTestVisible="False"
IsReadOnly="True"
FlowDirection="LeftToRight">
</TextBox>
<TextBox x:Name="FirstNameTextBox" Grid.Column="0" Text="{Binding FirstName, Mode=TwoWay}" TextAlignment="Left" HorizontalAlignment="Stretch"
materialdesign:HintAssist.Hint="FirstName" Style="{DynamicResource MaterialDesignFloatingHintTextBox}"
materialdesign:HintAssist.IsFloating="False"
materialdesign:HintAssist.HintOpacity="0.10"
TabIndex="0" Grid.ColumnSpan="3"
VerticalAlignment="Bottom"
Margin="10 0 0 0"
Opacity="0.001"/>
<TextBox x:Name="MiddleNameTextBox" Grid.Column="1" Text="{Binding MiddleName, Mode=TwoWay}" TextAlignment="Left" HorizontalAlignment="Stretch"
materialdesign:HintAssist.Hint="MiddleName" Style="{DynamicResource MaterialDesignFloatingHintTextBox}"
materialdesign:HintAssist.IsFloating="False"
materialdesign:HintAssist.HintOpacity="0.10"
Margin="10 0 0 0"
VerticalAlignment="Bottom"
TabIndex="1" Visibility="Collapsed"/>
<TextBox x:Name="LastNameTextBox" Grid.Column="2" Grid.Row="2" Text="{Binding LastName, Mode=TwoWay}" TextAlignment="Left" HorizontalAlignment="Stretch"
materialdesign:HintAssist.Hint="LastName" Style="{DynamicResource MaterialDesignFloatingHintTextBox}"
materialdesign:HintAssist.IsFloating="False"
materialdesign:HintAssist.HintOpacity="0.10"
VerticalAlignment="Bottom"
Margin="10 0 0 0"
TabIndex="2" Visibility="Collapsed"/>
</Grid>
<ControlTemplate.Triggers>
<Trigger Property="IsKeyboardFocusWithin" Value="True">
<Setter TargetName="FirstNameTextBox" Property="Opacity" Value="1"/>
<Setter TargetName="FirstNameTextBox" Property="Grid.ColumnSpan" Value="1"/>
<Setter TargetName="MiddleNameTextBox" Property="Visibility" Value="Visible"/>
<Setter TargetName="LastNameTextBox" Property="Visibility" Value="Visible"/>
<Setter TargetName="dummyTextBox" Property="Text" Value=" "/>
</Trigger>
<Trigger Property="IsKeyboardFocusWithin" Value="False">
<Setter TargetName="dummyTextBox" Property="Text" Value="{Binding Path=FullName, Mode=OneWay}"/>
</Trigger>
</ControlTemplate.Triggers>
</ControlTemplate>
<Style x:Key="MultiTextBox" TargetType="ContentControl">
<Setter Property="materialdesign:HintAssist.HintOpacity" Value="0.10"/>
<Setter Property="materialdesign:HintAssist.IsFloating" Value="False"/>
<Setter Property="materialdesign:HintAssist.FontFamily" Value="Century Gothic"/>
<Setter Property="materialdesign:ColorZoneAssist.Mode" Value="Dark"/>
<Setter Property="FontFamily" Value="Century Gothic"/>
<Setter Property="Foreground" Value="AliceBlue"/>
<Setter Property="FontSize" Value="20"/>
<Setter Property="FontWeight" Value="Normal"/>
<Setter Property="Margin" Value="10 0 0 0"/>
<Setter Property="IsTabStop" Value="False"/>
<Setter Property="Template" Value="{StaticResource MultiTextBoxTemplate}"/>
</Style>
</Window.Resources>
<Grid>
<Grid.Background>
<LinearGradientBrush EndPoint="0.5,1" StartPoint="0.5,0">
<GradientStop Color="#FF06013F" Offset="1"/>
<GradientStop Color="#FF040F2E"/>
</LinearGradientBrush>
</Grid.Background>
<StackPanel Orientation="Horizontal" HorizontalAlignment="Center" VerticalAlignment="Center" FlowDirection="LeftToRight">
<TextBox Style="{StaticResource MaterialDesignFloatingHintTextBox}"
Text="{Binding ID}"
materialdesign:HintAssist.Hint="ID"
materialdesign:HintAssist.HintOpacity="0.10"
materialdesign:HintAssist.IsFloating="False"
materialdesign:HintAssist.FontFamily="Century Gothic"
materialdesign:ColorZoneAssist.Mode="Dark"
FontFamily="Century Gothic"
Foreground="AliceBlue"
FontSize="20"
FontWeight="Normal"
Margin="0 0 0 0"
IsTabStop="False"/>
<ContentControl Style="{StaticResource MultiTextBox}"
materialdesign:HintAssist.Hint="FullName"
MinWidth="300"
MaxWidth="400"
VerticalAlignment="Bottom"
Content="{Binding Path=FullName}"/>
</StackPanel>
</Grid>
</Window>