Overriding code-generated DbContext constructor

I up-voted the previous accepted answer because it is a fairly elegant way of doing it. However another approach would be to modify the T4 template that generates the dbContext Class.

When using EF DB first you have a .edmx file and under that you have an [Entity].Context.tt file. Go into that file and remove (or modify) the following code:

public <#=code.Escape(container)#>()
        : base("name=<#=container.Name#>")
    {
<#
if (!loader.IsLazyLoadingEnabled(container))
{
#>
        this.Configuration.LazyLoadingEnabled = false;
<#
}

foreach (var entitySet in container.BaseEntitySets.OfType<EntitySet>())
{
    // Note: the DbSet members are defined below such that the getter and
    // setter always have the same accessibility as the DbSet definition
    if (Accessibility.ForReadOnlyProperty(entitySet) != "public")
    {
#>
        <#=codeStringGenerator.DbSetInitializer(entitySet)#>
<#
    }
}
#>

now your context class will generate without a constructor, so you should be able to go and create one in an extended class.

The best I can suggest is a factory method:

private HOLDbEntities(string contextName) : base(contextName) { }

public static HOLDbEntities Create() {
    return new HOLDbEntities(ContextName);
}

and use HOLDbEntities.Create() rather than new HOLDbEntities().