If you decide to use your name, this is fine, but you do need to be mindful of future requirements, goodwill in your business and succession plans. Julia's Bookkeeping may sound fine now, but in 10 years time, will someone see value in this as a name and want to buy the business?
I am not saying you can't or shouldn't use your name, but you need to keep in mind your future requirements.
Popular bookkeeping names have always come from bookkeeping and accounting terminology or associated words such as "Balanced Bookkeeping" or "Ledgers." These words are popular and can help you come up with ideas. An accounting or bookkeeping dictionary can also give you some ideas.
It is good to steer clear of negative connotations and use positive sounding words.
You can also do some research on the Internet on what what words people use when searching for a bookkeeping services. You can enter your words into google niche finder and see what other related words people are using. This will be helpful later when you are trying to get a better ranking in search engines. If your site contains words people use, it is helpful in improving your rankings. If you can get a good raking in google or a similar search engine organically, it is fantastic.
I hope this gives you some ideas to think about when deciding on your business name. These are just snippets of information about this topic and further information can be found in my book, My Bookkeeping Business - How to Start, Run and Grow your Bookkeeping Business.