Hi Jack

You need to create surface controller or api controller on backend code and form for members.

Try to look at this method:

[HttpPost]
public ActionResult HandleUpdatePassword([Bind(Prefix = "passwordModel")]UpdatePasswordModel model)
{
    try
    {
        if (ModelState.IsValid == false)
        {
            return CurrentUmbracoPage();
        }
        var memberService = Services.MemberService;
        var member = memberService.GetById(AppHelper.GetCurrentUserId());
        memberService.SavePassword(member, model.Password);
        TempData["UpdateSuccess"] = true;
    }
    catch { }
    return CurrentUmbracoPage();
}

It basically do what you need, adopt this code for your needs and it will work.

Read more about memberService, it has a lot of methods for working with members:

https://our.umbraco.org/documentation/reference/management/services/memberservice

Hope it will help.

Thanks.

Alex