Google's John Mueller said that when you merge two sites together, the domain you are getting rid of and not using anymore will take time to go away in Google's search results. When you do a site move, like moving to a new domain but it's the same content, URLs, etc, then that is much faster.
John Mueller said on Twitter "No, you don't have to do anything to get it removed - it just takes a lot longer when you merge sites rather than move domains. If you use the removal tools, you won't get any traffic at all for the old domain, so I'd recommend not doing that."
Here are some of the relevant tweets:
No, never use the removal tools for site-moves. The removal tool doesn't affect canonicalization, it won't speed up site moves. You'll get less traffic that way.
— 🍌 John 🍌 (@JohnMu) February 7, 2020
Those are completely different sites - and the query explicitly searches for the old site. This is not a site move; it looks more like you're merging sites. In my opinion, it's fine & expected for us to treat it like this.
— 🍌 John 🍌 (@JohnMu) February 8, 2020
No, you don't have to do anything to get it removed - it just takes a lot longer when you merge sites rather than move domains. If you use the removal tools, you won't get any traffic at all for the old domain, so I'd recommend not doing that.
— 🍌 John 🍌 (@JohnMu) February 8, 2020
Forum discussion at Twitter.