I understand this is not a technical question, I hope you don't mind.
Following are some vital bits of context as to why I have this dilemma:
I have been trying to think of a name for a year already.
I shoot pets, fish in particular.
I current use 4-5 text copyright notices. However, text is easy to remove.
Image theft is moderately common in fish photography.
Conclusion: following advice from another thread on this forum, I would at least like stolen images to contribute to my brand value. I think viewers would also appreciate 1 logo over 5 lines of text.
Current position: I have a typical 'MyName Photography' page with around 120 likes. I fear that if I hastily change the name, so I can pay someone to make me a logo, I might regret it later and have to do a 2nd rebranding.
Question: As a 'young' photographer and given the context, should I take the risk of a 2nd rebranding? Each time involves some investment and new social media accounts.
Better to do it early when you only have 120 followers than to wait until after you have more followers that you risk will not make the transition with you. You can ameliorate the risk somewhat by promoting the new brand on the older accounts for a while, including regular announcements that you are moving to the new account and will stop posting to the older one on a certain date.
By "page" I presume you mean Facebook Page.
I agree with Michael it is perhaps best to do it early, but some international companies change their branding, so it must be possible to do it later also.
Some thoughts and ideas - if you have corresponding domain names, then retain them (ie. even for the old name). You can configure your old brand to automatically forward to the new one (with or without a message to the site visitor explaining the redirect). This means anyone finding your old images and associated branding/URLs will still reach you at the new location.
Likewise, retain your old FB page and social media, at least for a while. Once you're set up on the new page/account, then promote all your images via the new account but then go in to your old account and share the new account's posts - again, with a note saying "Please note, I am sharing all new content through my new page at XYZ".
To the question of whether or not to take the risk - nobody can advise. It'll be your judgment call on what the benefits vs risks are. If you have a small client base at the moment, consider contacting each directly and asking them to update their links/info.
And when you say you might regret rebranding later, and have to do a 2nd rebranding, do you mean re-brand back to the original brand? Or to a 3rd, new identity?
PS. I have the same dilemma - promoting my photography via my name or via my location :/