Looks like you first need to come up with a name for the company. But before you can start thinking about that, you should write for yourself a branding / naming brief. You can find one here.
To brainstorm for names you can use the following approaches:
- First of all write down all the words that are related to the subject building on the brief. Synonyms, related concepts, etc
- Try a mash-up of words. Example: Lens + Mastering = MasterLens
- Get inspired by culture. Example: Nidaba is the god of learning: nidaba.photo
- Foreign languages. Especially latin. Example: Picha.io (image for swahili)
- Acronyms: LPO for Learn Photography Online
- Use the business owner’s name: Noelle’s Photography School
- Geographic location: Chicago Photo Classes
- Describe the business: Photoclass247
- Change spelling: Fotoclass
- Appeal to benefit: BestImage
- Talk about core values: StopTheTime
- Pick a related word: Aperture Photo School
- Think of other ways to brainstorm for words, the possibilities are endless
Come up with at least 50-100 ideas, then put them into a spreadsheet and add evaluate all of them one by one by the following criteria (you can add more):
- Short enough?
- Easy to remember?
- Is domain available?
- Descriptive?
- Is it different enough from competition?
- Etc. whatever fits your use case
Then assign a point or two (if important) to each, and then you add them up to get a total score for each name. This is a long and tedious exercise, but at the end you will be able to see the top 3-4 names. At this point you can work with each if you have such freedoms and see which one works best for the new identity.
Good luck!