I remember many (many, many) years ago having a cuppa with an inspector back when they still got to choose which businesses to visit rather than their computer telling them and that one, implying risen from the ashes, was always high on the hit list.
You will also need to check with your professsional body whether the name that you choose is allowable.
I had to change mine as the original business had the word Associates in it and I was informed in no uncertain terms that I could only call myself associates if I actually had associates.
On the using bits of your name to make up a business it certainly worked for Amstrad.
Google the name, check companies house to ensure that it's not like any existing names, try and get the website name, etc.
It may be worth trademarking the name espechially if you are not going to incorporate (take a look at the IPO site),
Good luck with the new venture,
kind regards,
Shaun.
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Shaun
Responses are not meant as a substitute for professional advice. Answers are intended as outline only the advice of a qualified professional with access to all relevant information should be sought before acting on any response given.
My suggestion is to make the IPO site your first port of call, because you can form a company and then find out that the name you have used is already trademarked. Nothing more annoying than having to go through a change of name process before you do anything else, unless it is being accused of "passing off" after you have begun to trade.
I don't see much wrong with simply using your own name: John Smith & Co or J Smith Bookkeeping & Payroll. If you want to use initials, then something like JS Bookkeeping & Payroll seems to fit the bill. Bookkeepers don't need fancy names.
I realise I stand to be corrected there, and you might want to find a catchy name that describes what you do and is also memorable. Maybe a reference to something like an abacus, a calculator, or a pay slip might work (although I'm sure those particular objects have already been used - it's hard to be original). I'm also sure the word numbers has already been pressed into service, but you might be able to think of another. Looking at your slogan (very amusing btw) you could try to work on Triple Entry or something???? (Not sure that'd work, on second thoughts.)
And there's also the regional aspect you could consider: perhaps, Knotty Ash Bookkeeping & Payroll
My final thought on this - but there are tons of other options if you think about it - is that there seems to be a fashion for internet-style names, so what about Books-and-payroll.com?
Final thought plus one - if you claim to be a national organisation, you'd better be. UK Bookkeeping and Payroll requires that you really do cover the UK.