acrobat keeps trying to update

Obviously, you didn't delete all of it completely, which is easy to do as it can embed itself deeply into your operating system.

In addition to moving the Adobe app to the Trash, you may find remnants of Adobe in the following locations:

• ~/Library/Application Support/
• ~/Library/Caches/
• ~/Library/Containers/
• ~/Library/Frameworks/
• ~/Library/Logs/Preferences/
• ~/Library/Saved Application State/
• ~/Library/WebKit/

To help discover their locations, I suggest using EtreCheck and run a report. You can either post the report here so we can assist you or go through it yourself to locate them.

Ref: Using EtreCheck to Troubleshoot Potential… - Apple Community

Did you try running an EtreCheck report as well and it didn't locate any other remnants? I would second Lexiepex's suggestion to remove it from Safari or any other web browsers that you use as well.

The other option is to create a new user account; log out of your existing account, and then, log back in with the new account to see if this issue continues. If it does not, you know that it is limited to your original account.

Even if you deleted everything, it seems their ad is still there.

If that is what is happening do this:

Shutdown Safari,

Start Safari while holding the Shift key (this passes by all caches),

In Safari->History: delete all history, then in

Safari->Preferences->Advanced: check "show develop menu", then in

Safari->Develop: "empty caches"

Now there should be no popups anymore.

From Dock : Launchpad : Other, open the Terminal application.

Find the most recent update to Adobe Acrobat Reader DC, and get detailed info

pkgutil --pkg-info $(pkgutil --pkgs | egrep -i -m1 acrordrdcupd)

Now get the date of its installation, by copy/pasting the integer following the install-time from the above output:

date -j -r 1566907600
Tue Aug 27 08:06:40 EDT 2019

You can get a listing of every file and folder created by that Adobe Acrobat Reader DC updater, and redirect that output to a text file on your Desktop, so that you can systematically check what has, and has not been removed. Some files may require administrator permission for removal.

pkgutil --files com.adobe.acrobat.AcroRdrDCUpd1901220040_MUI > ~/Desktop/Rdrdc_list.txt

Ignore it. You don't need that software on your Mac.