Surname change on ILR

Hello
if one wants to change their surname on ILR because of divorce happened abroad but got a deed poll would it be enough or the divorce paper also needs to be send along? And that too not from uk so do we need to apply for decree nisi?

Also ideally how long they take to send new card. Website says 6 months but will they send before 6 months?

You also need to change your passport.

If divorced legally by courts abroad there is no need to divorce gain in the UK.