Business registers in most countries are publicly searchable. You can search the relevant company register directly (Companies House in the UK, the SEC EDGAR or state registers in the US, the commercial register in EU countries) for newly incorporated businesses using a confusingly similar name.
Manual business register monitoring requires periodically searching through the relevant business register, and it’s most practical in only one or two key jurisdictions. For broader coverage, it’s recommended to go with third-party monitoring services, which can scan multiple business registers and alert you to all potential conflicts.
Note that a similarly named company alone does not automatically constitute trademark infringement; infringement requires use of the similar name in connection with the same or related goods or services in a market where you hold trademark rights.