Thank you for the question the simple answer is yes, you can do both clearly you have purchased the name which means the domain is free, you can also trademark it in the Uk and look at doing this internationally too. If the podcasts have not done this then they are basically slow to the mark. The reality is that they may never infringe upon each other. I would advise registering the trademark in asap. When you register the trademark the ICO will inform. you if there are any potential objections however this does not prevent you from moving forward with the application. In the event there is an objection to your application, it will be reviewed and you may still be able to register, if not, you could look at using the web address as a trading name as opposed to your company name. It may be preferable to have a solicito review your position in full detail.
I shall provide you with a helpful link that will assist you in finding a solicitor/representative near your local area. This will provide you with someone nearby your area who can assist you if required.
I hope this information proved helpful. You will find a local solicitor who deals with these matters on the law society webpage which is as follows;
https://www.lawsoc-ni.org/solicitors (N. Ireland)
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