Find DivTag element in list and click when innerHTML matches account name
To eliminate the need for the flag you could do it like this:

var element = _my_repo.SignInToYourAccount.UseAnotherAccount;
foreach (var item in _list)
{
    if (item.GetInnerHtml().Equals(_account_name))
    {
        element = item;
        break;
    }
}
element.Click();


However, your code can be greatly simplified with the Linq extension methods provided in the System.Linqnamespace: 

var element = _list.FirstOrDefault(x =&gt; x.GetInnerHtml().Equals(_account_name)) ?? _my_repo.SignInToYourAccount.UseAnotherAccount;
element.Click();