Unlike in many other countries, anyone in the UK is free to use whatever name they like, when they like. (That obviously excludes fraudulent activity, such as pretending to be someone else in order to cash a cheque in their name). There's no need for any deed polls. You can be Freda Smith on Monday mornings, Harry Fitzwilliam on Monday afternoons, Iggle-piggle-poodle-twinkie on all other weekdays, and His High Worthiness Prince Muzzelheimer the Fifteenth at weekends. It's all perfectly legal.
Obviously 'officialdom' likes you to to have one 'real' name (e.g. on your passport and bank accounts), so it's useful to have a formal way of changing your name (i.e. by deed poll) but there's no legal necessity for it.
Also (unlike in some other countries), there's no requirement for a married person to take their partner's surname. So there's certainly no need for one partner in any relationship to make changes to their own name in order to match that of their partner.
You can both use whatever names you choose. If those names are different to how you're currently known on your passports, at your banks and at other places that like you to have an 'official' name, then it would probably simplify things considerably if you used fresh deed polls but, as stated above, they're not a legal necessity.
Chris