The delete button is gone as seen in the image attatched. I want to delete it then reinstall it since I'm trying to join a server that requires mods. In my opinion I find it easier to delete the new one then install an older version of forged since downloading an older version without removing the updated version gives me troubles. It doesn't always update to the older version. And now i cant even rename or edit the installation besides resolution and game directory.
What you want to do is create a new profile, by the looks of things you have the Dirt block which is 'latest version' profiles (I assume you have two and you duplicated the profile but it is a 1.12.2 now besides the 1.14.3 it was for the prior), you'll want to create a new one which like the Forge one you have is a Furnace (icons don't matter but I'm just saying the default ones so you know what to expect when profile creating).
Go to the 'installations' (used to creating, deleting and managing profiles/installations) and select 'new' then name it maybe '1.12.2' or '1.14.4' or whatever version your after so it's nice and simple, select the version (release or Forge) then run it. This will run Vanilla yes but it's good to do this before ever installing Forge or another modloader like Fabric in 1.14 or Liteloader in 1.12.2. After it's done, then create a Forge one and add the Forge version for 1.14.4 you have there (if a Forge versions from 1.13+ it's among the 1.13 and 1.14 release versions, if 1.12.2 or prior of Forge it's below Release 1.0), while Forge may create it's own if you want you can just create your own and manage it that way so you know it is selected correctly to that Forge version you wanted it to be.
Run that and if it is successful then you can close the game and add the mods you want.
Profile deletion related and not Forge related like above:
By the looks of the duplication and the 'delete option' not showing up I'd say go to your .minecraft then your versions folder, then delete that profile you don't want that you have duplicated since I'm assuming you can't delete the latest release profiles since it's supposed to create one by default. But probably best to close your launcher before deleting that folder (the 1.12.2 one not the 1.14.3 one).
On another note:
If you don't want to make things complicated with the Vanilla launcher by working out profiles and modding the game and just want to use it for Vanilla I recommend the Twitch launcher since it's simpler and still uses the Vanilla one just quicker and easier to setup a modded profile/manage, add the mods you want (as long as your careful of the Fabric ones as well as, if your not check my signature for the forum wiki on Fabric below so you don't add Fabric mods to a Forge instance since they aren't compatible) and your good to go.