How to help the branded Uruk captain bully Uruk soldiers into joining him

To make sure that they stay dead, you need to behead them.

At least that's what the IGN Wiki tells me:

Death in the Nemesis System

Death is not the end in the Nemesis System: Not for Talion, and not always for the Uruks either. Whenever you kill a Captain or Warchief in Sauron's Army, there is a chance that they will survive the apparent killing blow. This can only happen if the Uruk in question was not beheaded in the finishing blow. Any Uruks that are lying down dead in the army page may come back and hunt Talion for revenge. After encountering them in the wild, they will reappear in the army page, now on their feet and sporting new scars based on their previous encounter. Some Uruks may even gain Strengths and Weaknesses depending on what happened to them.

In order to get an Uruk of your choosing to become a bodyguard you'll need to advance far enough into the story to issue commands to branded Uruks.

You will know how to do it by the time you finish that story mission, you also won't be able to do it before then.

Here's a reminder in case you forgot how it's done:

1. You need to brand a captain (the future bodyguard) using either Stealth Drain (if he's vulnerable to stealth), Combat Drain, or by choosing the "Dominate" option when you get the chance to finish him off.
2. Grab the branded future bodyguard and "Dominate" him (this is the same move as when you interrogate Uruks), then select the "Command" option.
3. Choose the warchief your captain is supposed to guard.
4. Start the captain's "Power Struggle" mission and help him if necessary.

Once the Power Struggle is complete, your captain will be promoted to bodyguard and be assigned to whichever warchief you chose earlier.

Uruk captains can also get promoted to bodyguard without your help, but you won't have control over who guards whom. Simply make sure every captain is branded, so the warchiefs can only choose branded Uruks to guard them.