I purchased a domain name I had in mind to set up a website, however there’s currently a blog (with a different domain name) that has the same title as my domain name, and covers the same topic.
Will that be an issue for me, apart from the fact that the blog comes up when someone searches for that domain name?
I prefer to be sure before registering a company name or taking any steps to protect the name
There are millions of sites out there that deal with similar topics; but as long as the content is not copied, but is put in your own words, there is no problem.
works for me, although the topic is similar none of the content will be comparable
Just make sure the blog in question isn’t trademarked, if their brand has a trademark associated with it you could be seen as infringing on their rights because you’re not only doing the same thing as them, your using the same name (which could lead to people mistaking your service for theirs) - and that can lead to legal trouble. If no trademark exists however you should have equal rights to the naming convention you choose. 
No sign of a trademark, in fact the blog is more of a diary, no service provided, unlike my planned site.
OK, then I would say you’re good to go, might just be worth putting on the about page (or terms of usage document) that you’re in no way associated with them
Good idea, thanks
If domain name is catchy and memorable and describes your business somehow I suppose that worth to register this domain name indeed.