Entity Framework change connection at runtime

DbContext has a constructor overload that accepts the name of a connection string or a connection string itself. Implement your own version and pass it to the base constructor:

public class MyDbContext : DbContext
{
    public MyDbContext( string nameOrConnectionString ) 
        : base( nameOrConnectionString )
    {
    }
}

Then simply pass the name of a configured connection string or a connection string itself when you instantiate your DbContext

var context = new MyDbContext( "..." );

A bit late on this answer but I think there's a potential way to do this with a neat little extension method. We can take advantage of the EF convention over configuration plus a few little framework calls.

Anyway, the commented code and example usage:

extension method class:

public static class ConnectionTools
{
    // all params are optional
    public static void ChangeDatabase(
        this DbContext source,
        string initialCatalog = "",
        string dataSource = "",
        string userId = "",
        string password = "",
        bool integratedSecuity = true,
        string configConnectionStringName = "") 
        /* this would be used if the
        *  connectionString name varied from 
        *  the base EF class name */
    {
        try
        {
            // use the const name if it's not null, otherwise
            // using the convention of connection string = EF contextname
            // grab the type name and we're done
            var configNameEf = string.IsNullOrEmpty(configConnectionStringName)
                ? source.GetType().Name 
                : configConnectionStringName;

            // add a reference to System.Configuration
            var entityCnxStringBuilder = new EntityConnectionStringBuilder
                (System.Configuration.ConfigurationManager
                    .ConnectionStrings[configNameEf].ConnectionString);

            // init the sqlbuilder with the full EF connectionstring cargo
            var sqlCnxStringBuilder = new SqlConnectionStringBuilder
                (entityCnxStringBuilder.ProviderConnectionString);

            // only populate parameters with values if added
            if (!string.IsNullOrEmpty(initialCatalog))
                sqlCnxStringBuilder.InitialCatalog = initialCatalog;
            if (!string.IsNullOrEmpty(dataSource))
                sqlCnxStringBuilder.DataSource = dataSource;
            if (!string.IsNullOrEmpty(userId))
                sqlCnxStringBuilder.UserID = userId;
            if (!string.IsNullOrEmpty(password))
                sqlCnxStringBuilder.Password = password;

            // set the integrated security status
            sqlCnxStringBuilder.IntegratedSecurity = integratedSecuity;

            // now flip the properties that were changed
            source.Database.Connection.ConnectionString 
                = sqlCnxStringBuilder.ConnectionString;
        }
        catch (Exception ex)
        {
            // set log item if required
        }
    }
}

basic usage:

// assumes a connectionString name in .config of MyDbEntities
var selectedDb = new MyDbEntities();
// so only reference the changed properties
// using the object parameters by name
selectedDb.ChangeDatabase
    (
        initialCatalog: "name-of-another-initialcatalog",
        userId: "jackthelady",
        password: "nomoresecrets",
        dataSource: @".\sqlexpress" // could be ip address 120.273.435.167 etc
    );

I know you already have the basic functionality in place, but thought this would add a little diversity.