"our client has been using this name and logo (very similar to my uncle's) since 1994 and you have no right to use it". Thing is, my uncle founded his company in 1986 and had the current logo done in either 88 or 89.
It's an illustration of why it's important to keep records...
From what you say it would seem your uncle took up the trading name (trading style) before the complainant, therefore he has he right to continue doing so, and it is the complainant who would find themselves on the wrong end of a 'passing off' action should this go to court - indeed it is they who should be 'ceasing and desisting' as they're (arguably) trading on your uncle's goodwill.
Additionally, the logo is protected by copyright law.
It's not necessary - but it makes life easier - if you register your trading name as a limited company; you can keep said company dormant and 'licence' the name back from it (provided there is no financial exchange) to avoid complexity or making your affairs 'too public'. These days, registering the .com domain name at an early stage is also an essential. In fact I'd go so far as to say that if you cannot get the .com for a new business name, pick something else! - If you get letterheads or the like done, keep the invoice 'forever' with a sample of the letterhead etc.
Ultimately, these things (theoretically at least) wind up in court to be sorted out. - Which isn't good. But in this sort of situaiotn, let them go to the expense of raising the action - send them your evidence first though; I doubt any sane solicitor would let them get that far and ultimately they might be told by their own legal team to 'take down' the name.