Trademarking: tips and pitfalls

[Stakhanovite]

I'm looking to trademark a catchy name I've come up with for a particular way I approach content creation (which is the main service I offer). And ideally I'd like to do it for UK and US.

I can see there are ways to do this online, but keen for any advice on best way to do it? Any pitfalls to avoid?

In the UK do it yourself via www.gov.uk don't pay an agency to do it.
In the US it may be just as simple or you may need an agent. I've only done UK ones so can't say for sure.

Many thanks, @DelilahBucket