Millrace Translations makes its mark!
For several reasons, it can be a good idea to register your business name and/or logo as a trade mark
it shows you take your business seriously and are prepared to invest in its brand
intellectual property is an asset of your business (ask your accountant)
it may be prudent to "get in first" to avoid someone later using and registering the same or a similar name and/or logo in the same professional field, which could be very awkward if you have built up an established business
you will probably find out in the process of researching and registering your trade mark, whether you are unwittingly treading on someone else's toes (maybe there is a huge multinational with the same or similar name in the same professional field), in which case it's better to find this out sooner rather than later
in most cases registering your trade mark yourself is straightforward and reasonably priced
the UKIPO provides information and a certain level of free support
the British Library also has information and tips for newbies
don't just take my word for it! Post here by the Chartered Institute of Trade Mark Attorneys
Looking to the future, if your business has a name separate from your own, this makes eventual sale of the business simpler, and registering the name as a trade mark makes it more attractive. You can register your own name as a trade mark, although there is no automatic right to one (see post here from BeckGreener).
What you can register (copied from UKIPO)
Your trade mark must be unique. It can include:
words
sounds
logos
colours
a combination of any of these
There are also some things you can't register, listed on the same page.
Why not start by having a look at trade marks already registered in your professional area - as above, this could be in Class 41 (translation, etc. services). Here is the search page.
Trade marks registered in the EU can be searched here. A separate application is required for an EUTM.
Millrace Translations' trade mark is a "figurative" mark, covering the words in a graphical context. A "word" mark can also be chosen, protecting the word or words applied for. This piece by Safenames describes differences between word and figurative marks.
Of course, you can always ask a Chartered Trade Mark Attorney for advice - here is CITMA's dedicated page.