I like how in the creation of custom backgrounds, there are options in creating variants of the background features. However, I was wondering, as a player, if it's possible to choose the variant feature for the background rather than the default feature. For instance in the Noble background, there is the variant feature of Retainers, but I'm unable to choose that feature during character creation instead of the Position of Privilege default feature. 

In the creation of homebrew backgrounds, you are able to make variant features as well, but I'm unable to choose said variant feature during character creation. Is this something the player has to keep track of separately in their notes section or is there a way for it to automatically be shown in the character sheet? Thanks!

You will need to make it a custom. There's 2 ways to do this: a temporary way, and a permanent way.

Temporary way:

When in Character Creation under description choosing background in the drop down choose "custom background".

Name it something suitable like "Noble (Variant)".

In the descrption box you can copy the Noble's text (for reference open a new tab to: https://www.dndbeyond.com/characters/backgrounds/noble).

For Proficiency/Language Choice choose "2 skills, 1 tool, 1 language".

For Background feature choose "Knight."

For Background Characteristics choose "Noble".

Save.

Now you can scroll down and can select the 2 skills, choose History and Persuasion or any of your choosing if you have proficiency from elsewhere.

You can choose a tool of your choice but to fit with the Noble choose a gaming set.

You can choose a language of your choice.

The Retainers background feature will be selected for you. You can then choose the characteristics from the Noble list as normal.

This creates a custom background specific for your character.

For the permanent way:

Ccreate a homebrew background by going here: https://www.dndbeyond.com/homebrew/creations/create-background.

For "use an existing background" select Noble. Name it something suitable like "Noble (Variant)".

Where it says Feature Name put in retainers. Where it says Feature Description copy the Retainers feature text from the Knight background: https://www.dndbeyond.com/characters/backgrounds/knight.

Remove everything from the "variant" boxes referring to the knight.

Save.

Your new Noble (Variant) can now be used on future characters.

What about if you want to use the variant features from Van Richten's Guide to Ravenloft?