The new Infinite Potions don't respect the effort of an adventurer. One can just leech weekly quests and get infinite potions without any effort. Another instead can spend a lot of hours getting raw pieces to prove to everyone and him/herself that he/she doesn't require any help, such as a pity system. However, at the very end, they end up with the same exact item. This is incorrect and not respectful to the adventurer putting relevant effort into the game. 

My suggestion is to add the ancienttag for the potions that have been completed using only ancient pieces.

Moreover, I understand the achievement of the adventurers that completed the infinite potions before the introduction of the pities, and thus, the reworked ancient potions shouldn't have the name of the adventurer on them, and shouldn't provide the old titles.

Is that not how it already works? when the raw piece drops, it has an anicent tag on the raw item, which you can use to make the ancient small potion, and upgrade to the bigger ones when you get the other ancient raw pieces. If you decide to combine a pity item with an ancient item, you have to trade in the ancient version for the pity version in order to use them together.

... If you leeched off weeklies for the entire pot it would actually be ancient by the time you got it.

Unfortunately not, I can tell you more: it's confusing and misleading. Cause if you get a raw piece with the ancient tag and you mix it with Everlasting Water, you will get Ancient Blessed Spirit Essence (https://bdocodex.com/us/item/40738/). At this point, you can only continue with raw pieces. Thus, if you mix Ancient Blessed Spirit Essence with another raw piece, you will get Ancient Greater Blessed Spirit Essence (https://bdocodex.com/us/item/40743/). So far, so good, but at the very end, if you combine the last raw piece with Ancient Greater Blessed Spirit Essence, you will get Ornette's Spirit Essence without the ancient tag. If you follow the patterns in bdocodex you can also check it.

As I said, this is confusing and misleading, but also unnecessary. Why would you get "ancient" pieces if you cannot obtain the Ancient potion? 

I have not got that far yet, I only have the Ancient Blessed Spirit Essence so far, but if the end result is Ornette's Spirit Essence, then that sounds like a bug because there is no point in having ancient tags on the ingrediants, and even less point in giving players the option to trade in and sacrifice their ancient tag item if they want to upgrade it with a pity piece. I would suggest submitting a ticket.

It's not a bug. It's how it is now, sadly. Plus, we won't get any help from all the people that already got the ancient one (of course they have to flex their potion and who cares about the others) . So, I guess it will stay like it is, with people flexing singular ancient pieces on the chat to prove their effort in grinding the potion.

Indeed it's not a bug. When pity system was introduced, everyone making the potions after, get normal potion without tag, no matter if you used full pieces.