I would appreciate some branding advise related to having inconsistent domain names handles on social media and other platforms

Tldr: Should I officially change all my domains and handles to be consistent, when people already have my existing urls etc? How should I let people know about the change?

For reference, I’m still very early in my business journey, and I don’t have much of a following yet. So this is a good time to be making these changes.

More info:

To demonstrate my dilemma, I’m going to use a fake business name (with a similar word formation). My fake business name is “The Philosophy Garden”. My current website is PhilosophyGarden .org, and I originally got matching social media handles for Facebook and Twitter: @ PhilosophyGarden. But this wasn’t available when I joined Instagram, so I got @ ThePhilosophyGarden on IG.

I recently created TikTok & YouTube accounts, and decided to make the handles match IG (since that’s where I’m most active). And I decided to change my Facebook page handle to match, since I am not very active there. (I don’t care about Twitter, since I don’t use it anymore.)

Thus, now all my main social media handles are the same: @ ThePhilosophyGarden. However, I’m still use “PhilosophyGarden” for other things: my website, gmail, linktree, patreon, and PayPal link.

So my question: should I also change these to match @ ThePhilosophyGarden?? And is so, how should I let people know about the change?

I already purchased the new domain (ThePhilosophyGarden .org), and I will keep the old one – so at least it can redirect. And I can create a new gmail to do the same. But for some of the others, I don’t think I could create a redirect. So I would have to either change the url, or manage 2 accounts for both urls (and this may not be allowed for some of them).

[Edit to add: I just tried to register the new gmail account (for ThePhilosophyGarden @gmail. com), and that handle isn’t available. So since that will have to stay as “PhilosophyGarden”, maybe it’s ok if my other URLs also stay the same, even even though the social media handles are @ ThePhilosophyGarden??]

What do you recommend?

I will add that I also have another planned business project with a different name, and I have obtained a whole set of matching domains and handles for that. So when I eventually launch that, I will reassess my branding strategy then (and to see which business name I am more recognized for).