This post demonstrates the different ways you can customize the migrations history table in EF Core.

The simplest scenario is when you just want to change the table name or schema. This can be done using the MigrationsHistoryTable method in OnConfiguring (or ConfigureServices on ASP.NET Core). Here is an example.

protected override void OnConfiguring(DbContextOptionsBuilder options)
    => options.UseSqlServer(
        connectionString,
        x => x.MigrationsHistoryTable("__MyMigrationsHistory", "mySchema"));

You can also customize the columns, but this is a bit more involved. You need to override and replace the provider-specific IHistoryRepository service. If the provider uses the base HistoryRepository implementation, you can customize the columns by overriding the ConfigureTable method. Here is an example of changing the MigrationId column name to Id.

protected override void OnConfiguring(DbContextOptionsBuilder options)
    => options
        .UseSqlServer(connectionString)
        .ReplaceService<SqlServerHistoryRepository, MyHistoryRepository>();
class MyHistoryRepository : SqlServerHistoryRepository
{
    public MyHistoryRepository(
        IDatabaseCreator databaseCreator, IRawSqlCommandBuilder rawSqlCommandBuilder,
        ISqlServerConnection connection, IDbContextOptions options,
        IMigrationsModelDiffer modelDiffer,
        IMigrationsSqlGenerator migrationsSqlGenerator,
        IRelationalAnnotationProvider annotations,
        ISqlGenerationHelper sqlGenerationHelper)
        : base(databaseCreator, rawSqlCommandBuilder, connection, options,
            modelDiffer, migrationsSqlGenerator, annotations, sqlGenerationHelper)
    {
    }

    protected override void ConfigureTable(EntityTypeBuilder<HistoryRow> history)
    {
        base.ConfigureTable(history);

        history.Property(h => h.MigrationId).HasColumnName("Id");
    }
}