You have only to change the YouTube settings to stop that from happening. I forgot how to do that but I will check it out and be back. 

Check this out John Mosier 

https://www.digitalbard.com/how-to-stop-unrelated-videos-from-showing-up-at-the-end-of-your-youtube-video/

If that does not get you where you want to be, contact Peter Mark 

Think twice about not using YouTube for videos, there is a lot of juice to be lost if you don't. 

Change the settings on YouTube.  But keep an eye on them, YT will change them back.

Vimeo!  What Ron and Alexandra Seigel said.  It is the preferred video site for professionals.  The only downside is that you may drop in Google SERPS.  

I wrote an earlier post on this, but I guess when you add another answer it wipes the old one out.  I use Vimeo and it is easy to use with Wordpress.  I did one today - check out the video on the bottom of this page.  If you need help, let me know happy to show you what to do.  With Vimeo it is very easy to embed their video files onto WordPress.

I should add putting videos on YouTube makes sense too, just not linked on your site, but for  search. 

I use YouTube for the SEO traffic, John. Just change your settings so that others' videos don't follow yours.

beyond my paygrade..... If I wanted that setup, I'd be calling Katerina Gasset 

Clicking just one box on the embed link will prevent those other previews.

Beyond that, stick with youtube, your viewers will appreciate not having to allow some other site access to their computer.

There are other options in know but I choose to let them reside on YouTube for the Google juice boost.

John,

I have no idea, but what I do know is that even if it hosted on your website, it has to be hosted by another company.  We use Vimeo, and pay the extra for not having their logo on our videos.  It is how every one I know does it...A

Unless you have your own server to host it on, you can buy a server it is not worth doing your own, according to Ron because of all the different Internet speeds and different devices.  A

YouTube has the best SEO on the planet.  Vimeo is next. 

But in order to get SEO, you can not just host your videos on your website. you have to embed them on your website after they have been SEO'd on a video platform that Google bots like to crawl. 

You will need the paid version of Vimeo to do a little like what you can do on YT. 

If you don't want to share related videos on your YouTube embedded video, just turn those off in your YouTube settings. 

You can change that John with the flip of a switch. Do not let them 'suggest' other videos.

Easily just uncheck a box. Don't blow a head gasket over what you can easily do.

Does anyone know? Judging from the answers received,  I'd respond in the. affirmative.  It appears to this non-tech gut that there are many good answers. 

You've received a lot of good answers here. John. I can't add to them.

Not me...

You have some good advice.

How about Vimeo?

Thanks for the Q.

I would have no idea, but I prefer my videos up on You Tube.

John Mosier - excellent answer from Kathleen Daniels. 

Good luck.

no

https://wordpress.org/plugins/flowplayer6-video-player/

Great question John Mosier and good stuff Kathleen Daniels thanks for the details. Learning here too. 

Above my level of knowledge, but the gurus here in the Rain will provide good advice. I will be reading!

I don't.

It has been   a time since I set one up