For anyone else with this issue...Tech Support instructed me to delete my preferences folder and let C4D create a new one and then move my plugins and layouts and other personal preferences back into the new one. This fixed my problem.
I will list the instructions I received here, but I would suggest anyone with a similar issue to contact Tech Support for personal guidance.

FIRST-Can you go to your Program Files folder (Windows)/Applications folder (Mac), and rename the Maxon Cinema 4D 2023 folder to Maxon Cinema 4D 2023.2, then relaunch Cinema 4D?

What this will do is non-destructively create a new set of preferences. If the issue is not present after this change, we can confirm the issue is with the preferences and troubleshoot the preferences; if the problem is still present, you can rename the folder back to Maxon Cinema 4D 2023.

IF THIS DOES SOLVE THE PROBLEM-It's difficult to pinpoint the exact cause since I haven't encountered this issue before, but my guess would be the C:\Users*USERNAME*\AppData\Roaming\Maxon\Maxon Cinema 4D 2023_********\prefs folder in the preferences.

It's important to note that the prefs folder contains your custom UI color changes, custom shortcuts (if you've made any), and any changes made to the preferences window (Edit > Preferences in Cinema 4D). For example, if you've added a custom path for your plugins, that information would be stored in the Maxon Cinema 4D 2023_******** / prefs / Cinema 4D.prf file. Deleting the Cinema 4D.prf file would revert preference settings back to default.

With that said, I've provided instructions below that I typically share after determining that preferences might be the issue. Essentially, this involves deleting the preferences, but I've also listed folders you may want to keep, as they store custom settings if you've made any changes.

However, since I'm not aware of all your customized settings, you may also want to review this FAQ:
Where are my custom layouts, assets, plugins, shortcuts, etc., stored in the Cinema 4D preferences?

It will help you understand where customization information is stored in your Cinema 4D preferences folder and which folders you may want to avoid deleting:

The other, more tedious option, if you're concerned about losing custom settings, is to copy all the folders from within the Maxon Cinema 4D 2023_******** folder, place them somewhere easy to access, then delete all files and folders in your Maxon Cinema 4D 2023_******** preferences folder, and re-add them one by one, testing each time you re-add a folder.

Here is how to delete your Cinema 4D preferences:

You can delete your preferences by going to:
Edit > Preferences in Cinema 4D

When the preferences window opens, click the "Preference Folder..." button on the bottom left. Once open, quit Cinema 4D (this is a crucial step as this process will not work if the application is running).

Next, delete all the folders in the preference folder (**READ BOLD PRINT BELOW BEFORE YOU DELETE). Now, when you re-open Cinema 4D, it will create all-new preferences and hopefully get you past the issues you are experiencing.

**To start, if you've just installed a fresh copy of Cinema 4D and have not added any plugins, creating custom layouts, added custom assets to your asset browser, etc., you are safe to delete the entire folder without issues. If this is not a fresh install, the following information is meant to prevent you from deleting anything you probably do not what to delete.

To save you from reinstalling/rebuilding plugins, layouts, imported assets, etc., below are the folders you can leave unless we've identified the issue coming from within one of these folders:
MAXON\Cinema 4D R2*********\plugins
MAXON\Cinema 4D R2*\library
MAXON\Maxon Cinema 4D R2*_\userrepository
MAXON\Maxon Cinema 4D R2*********\description.db
MAXON\Maxon Cinema 4D R2*\dc
MAXON\Maxon Cinema 4D R2*_\cvToolbox (if Cineversity plugins are installed)

I should also note that the MAXON\Maxon Cinema 4D R2*_********\prefs folder is where your preferences settings are stored. For example, if you disable the Quickstart menu from popping up and delete this folder, the Quickstart menu will reappear again when relaunching Cinema 4D.

More often than not, if the preferences cause the issues, the files in the prefs folder are the culprit. So if you've made any changes in the Cinema 4D preferences window, such as the Quickstart example I mentioned, they will be stored in this folder.
In most cases, it's not a big deal to remove, but I just wanted to inform you that you would be reverting all settings to default.

However, if you made numerous changes in the preference settings, another option would be to simply move all files and folders from the preference folder, store them somewhere easy to find, such as the Desktop, and restart Cinema 4D. Cinema 4D will rebuild a fresh set of preferences upon launch. If the issue persists, you can quickly put the preferences back without losing the work you've done customizing the preferences.

Normally I would not use numbers at the end of the name I created, although I have tried that specifically using Name-01_ with the same results. I would usually just use Name_ and let C4D fill in the frame numbers.
I have recorded a quick screen capture video of the issue for Tech Support, would you like me to upload it here as well?

@Dr-Sassi said in pyro output cache or cache scene "specified name already exists":

Hi Mike,

Thanks for checking with support. If there is a problem, it should be solved.

I can't reproduce this here, but I have to ask, you do not use numbers at the end of the name. If so, put an underscore after the number. Name-01_

All the best

Thank you for your time. I will contact tech support.

Its not that it will not apply the new name. It is the sequencing of the number at the end that it does automatically. It actually does work but for some reason it thinks it overwriting the first file in the sequence.

All the best,
Mike

Whenever I try to Cache a Pyro Output I get the error that the specified name already exists , "Default Simulation Scene.000, do I wish to overwrite, yes/no". I do get all of the vdb files no matter which choice I make. Yes takes longer though. Then I have to make this choice for every frame. I've tried using the default name or a new unique name in a new unique folder.
If I export the scene as a File/Export/ Volume (*.vdb) it seems to work fine.
Also what is the difference between Cache Scene and Cache?