Under the Data Protection Act 2018 you have the right to be forgotten, also known as the right to erasure of your personal data. Personal data refers to any information which can be used to identify you.
Under the right to be forgotten you have the right to request search engine operators, typically Google, to remove your personal data from their search engines. This may also include requesting the delisting of search results which hold your personal data. Many search engines have their own standard form which you can use to request your data be removed.
You may also wish to submit a subject access request, asking a company what personal data it holds. Should you be concerned by this you can then exercise your right to erasure or amendment of personal data to either remove or correct the record.
The Information Commissioner’s Office, the United Kingdom’s Data Protection Authority, has details of your right to erasure here. For more details of your data protection rights see the Government Guidance here.