LLC and Business Name and Tax
Also for tax purposes if it is single member LLC I can just do a Schedule C?
In your situation, why complicate things by using multiple name? Just register your LLC as "Richard Lastname Photography LLC" and market yourself as such. There is no point of having a company under a different name if the "Photography" name is the one you really want to use.
Otherwise, consider getting a DBA name in the alternative name you want to use for your business. A DBA name does not have to use the "LLC" extension. For example, you can be "Richard Lastname LLC d.b.a. Richard Lastname Photography" and market yourself as "Richard Lastname Photography."
As for your tax question, please remember to consult your accountant on all issues relating to taxes. From our general knowledge, you can file the Schedule C as a single-member LLC.