Another thing to take into consideration is your audience. Who are you marketing your services towards? If I’m marketing my VO services towards high-end clients on my website, I do not want them to see any Fiverr branding or links on my website. Why? Because Fiverr is Fiverr - and is considered among many professionals to offer cheap, low to mid-range quality (even though this is less true today than it was back in the day), the Fiverr branding/name can be a negative influence if your target audience is high-end.
The same can be said the other way around.
When it comes to marketing on your own website - this is very similar to marketing on Fiverr. You’re doing SEO in your gig description, creating videos to market your gig and services, putting together nice graphics to pull in leads, and sharing all that in social media. That isn’t very different from how you would market a website.
My point is: if you already have the lead on your website, then why would you send them to Fiverr? If the client is already on your website, and ready to click “Order Now!”, why would that button lead to a platform that charges 20%? It should lead to professional payment processor (if you charge up-front), or to a form for more information.
If you don’t have a website, or if your website have no leads, then why market your Fiverr gig there anyway?
I don’t see many benefits to marketing Fiverr gigs on websites where you can reach clients without it. Less is more.
What you should do, in my opinion, if you want to market your Fiverr gig, is set up a professional landing page, that is meant only to lead people to your Fiverr gig, and market that with PPC and social media campaigns.
There are good ways of doing this, if you want to market your gig and become successful on Fiverr. But in my opinion, your professional website should be separate from that.