I spent months coming up with a great name for my business and brought all four domains so no one could steal it:
I have just seen there is someone on shopify using one of my domain names - mamababa.co.uk as her site domain, now if i set mine up with the same this will confuse any customers.
What can i do about this? as she clearly does not own the domain she is using as i have proof of ownership.
Since the registrar from this domain is GoDaddy.com, LLC you should try contacting their customer support and they may have a solution for you.
You can find out information like this using a WHOIS lookup tool such as this one: https://www.nominet.uk/whois/
You might also consider contacting the registrar you purchased them from.