So it turns out that the entity type is literally not known, or knowable, at compile time. It has to be a string.  
The only place you're using the type at compile time is in the cast to (DbSet<tableEntity>). Well, you may not need that. All you need from that type is to call AsQueryable(), and AsQueryable() is an extension method for IEnumerable, with generic and non-generic versions. IF we call it through non-generic IEnumerable, that's non-generic AsQueryable(), returning non-generic IQueryable. But we're returning object anyway, so hey. For the result of this thing to be useful, something somewhere must be doing a fair amount of reflection on it anyway, so the declared type is likely to be of little consequence. 
See if this works:
public object GetList(string typeName)
{
    Type tableEntity = Type.GetType("TestProject." + typeName + ", TestProject");
    var dbObject = (System.Collections.IEnumerable)
                        typeof(DbContext).GetMethod("Set", Type.EmptyTypes)
                        .MakeGenericMethod(tableEntity)
                        .Invoke(databaseContext, null);
    return dbObject.AsQueryable();            
}
If it turns out you need generic IQueryable<TEntityType>, we'll have to use reflection to get MethodInfo for AsQueryable<TEntityType> for the unknown (at compile time) entity type, and call MakeGenericMethod(tableEntity) on that. 
First try:
In the language, type parameters to generics must be actual types, not instances of the Type class. That's because they're resolved at compile time. 
But that's no problem; to pass a type parameter to a generic method, simply write a generic method with a type parameter. 
You can't do this:
var stuff = GetList("MyTableEntityClass");
But this is just as good:
var stuff = GetList<MyTableEntityClass>();
...
public object GetList<TTableEntity>()
{
    var dbObject = (DbSet<TTableEntity>)typeof(DbContext)
                        .GetMethod("Set", Type.EmptyTypes)
                        .MakeGenericMethod(typeof(TTableEntity))
                        .Invoke(databaseContext, null);
    return dbObject.AsQueryable();            
}
Reflection is different; that's why we pass typeof(TTableEntity) to MakeGenericMethod(). 
And once we're using an actual type that the compiler can check, we can do better with our return type, too:
public IQueryable<TTableEntity> GetList<TTableEntity>()
{
    var dbObject = (DbSet<TTableEntity>)typeof(DbContext)
                        .GetMethod("Set", Type.EmptyTypes)
                        .MakeGenericMethod(typeof(TTableEntity))
                        .Invoke(databaseContext, null);
    return dbObject.AsQueryable();            
}