Emojis are standardized by the Unicode Consortium so they are the same on all devices. Apple is not creating the standard for the emojis you see on your iPhone. All phone manufactures simply adopt the latest emojis that have been approved by the Unicode Consortium. If that was not the case, then an emoji you send on your iPhone, may show up as something completely different on a phone that does not use that same emoji. You can find more information on these standards here:
https://www.unicode.org/consortium/consort.html
What Apple does provide is the ability to create your very own Memoji for personalization. These are actually sent as small pictures (stickers) instead of an emoji, so they will appear on all devices.
Use Memoji on your iPhone or iPad Pro - Apple Support
In addition if you have a newer phone, you have the ability to create Genmoji's that are similar to a Memoji, but allows further customization by using spoken words for how you want it to appear.
Create your own emoji with Genmoji on iPhone - Apple Support
My recommendation is to use Memoji where you will have far more customization options than are available in the emoji set. You can use these in Messages just like an emoji.