I'm not sure if you are writing from the USA or UK, (or indeed some other jurisdiction) so I'll try and cover both legal standpoints.
As you know copyright is a personal property right, which just as with other property rights, you may retain, sell or otherwise dispose of as you wish. So if you assigned your copyright in a particular image to, say, a magazine, the chain of ownership (or 'title' in legal jargon) would follow the documentary trail. For the magazine to have 'good title' they would need to show that they had legally acquired the right from you (both US and UK law require that this is done in writing), and that you in turn had a legitimate claim to copyright as the author of the image in the first place. In both legal systems, copyright exists as a matter of fact when the image is created, presupposing that it has sufficient originality to qualify for copyright.
It doesn't really matter what name you wish to use in connection with that claim as long as you can show sufficient evidence that your legal name and your pseudonym refer to the same person. So for instance with a photograph, a crucial piece of evidence of authorship might be the original digital file, say a RAW image file with its attendant metadata, or a film negative. Mere possession of that source file would be credible evidence before a court, irrespective of the name of the owner. This is because in all countries which have signed up to the Berne Convention, no registration of the work is required in order to activate copyright. As you mention, the USA has a system of copyright registration which is optional in the sense that a work does not need to be registered to qualify, although it does need to be registered to bring an infringement action in the Federal courts. However the major advantage of registering your copyright in the US is that once the process has been correctly completed, registration is prima facie evidence of the validity of the copyright and of the facts stated in the certificate of registration. This applies whether the applicant is a US national or a national of another country. The US Copyright Office application form allows for the use of pseudonyms*, and so once a registration form containing both the legal name and pseudonym has been processed, this would be all the evidence of this fact that a court would need, in order to accept that Craig Charles Smith Weiner and Craig C Smith were one and the same, in addition to being the original owner of the copyright.
Of course in the UK there is no formal system of registration of copyright, and so a court would probably require an affidavit to the effect that the legal name and pseudonym referred to the same person.
Occasionally, the true identity behind a pseudonym becomes lost, in which case the law in the UK and the US takes different paths. UK law (Section 57 of the Copyright Designs and Patents Act 1988) applies the following formula when calculating the copyright term:
57 Anonymous or pseudonymous works: acts permitted on assumptions as to expiry of copyright or death of author.
(1) Copyright in a literary, dramatic, musical or artistic work is not infringed by an act done at a time when, or in pursuance of arrangements made at a time whenâ€”
- (a) it is not possible by reasonable inquiry to ascertain the identity of the author, and
(b) it is reasonable to assumeâ€”
- (i) that copyright has expired, or
(ii) that the author died 70 years or more before the beginning of the calendar year in which the act is done or the arrangements are made.
In contrast, US law (Title 17 USC Â§ 302c) says the following:
(c) Anonymous Works, Pseudonymous Works, and Works Made for Hire.â€” In the case of an anonymous work, a pseudonymous work, or a work made for hire, the copyright endures for a term of 95 years from the year of its first publication, or a term of 120 years from the year of its creation, whichever expires first. If, before the end of such term, the identity of one or more of the authors of an anonymous or pseudonymous work is revealed in the records of a registration made for that work under subsections (a) or (d) of section 408, or in the records provided by this subsection, the copyright in the work endures for the term specified by subsection (a) or (b), based on the life of the author or authors whose identity has been revealed. Any person having an interest in the copyright in an anonymous or pseudonymous work may at any time record, in records to be maintained by the Copyright Office for that purpose, a statement identifying one or more authors of the work; the statement shall also identify the person filing it, the nature of that personâ€™s interest, the source of the information recorded, and the particular work affected, and shall comply in form and content with requirements that the Register of Copyrights shall prescribe by regulation.
The final point worth noting is that while putting a copyright notice on your work is not legally required in either jurisdiction, there are some advantages to this. So if you put Â© Craig C Smith 2015
on one of your images there are two primary benefits: a) it advertises the fact that someone is asserting their copyright, and b) it helps a viewer of the image to contact you with regard to that copyright. Clearly if conventional searches via Google or telephone books etc fail to locate Craig C Smith then this second purpose is defeated. Obviously this wouldn't be a problem in your case if your website and social media accounts are in your professional name.
* The Compendium of [US] Copyright Office Practices contains the following explanation:
615.01 (b) Name of author: pseudonymous works - completing the space.
Where a work is pseudonymous, the applicant may:
1) leave the name-of-author space blank on the application and check the pseudonymous box: "Yes,"
2) give the pseudonym and identify it as such, or
3) give the author's legal name, preferably making clear which is the real name and which is the pseudonym, as for example: "Judith Barton, whose pseudonym is Madeline Elster."