When deciding whether a name is 'the same as' another name, the Registrar ignores punctuation, the company's status, 'the' at the start of the name, and words like 'company (or co)', 'and (or &) company (or co)'.
A name that sounds the same as one already on the Company Names Index may be accepted if the two names are spelt differently.
For example, if the name 'Hands Limited' is already registered, then the following would be rejected:
Hands Public Limited Company (or PLC)
H and S Limited (or Ltd)
H and S Public Limited Company (or PLC)
H & S Limited (or Ltd)
any of the above, with the addition of 'Company (or Co)' or 'and (or &) Company (or Co)'
So not easy to get the name you want, I suspect that domain names would follow the same guidelines (rules) but when looking for domain names the search you do is for the one you want, not similar ones that may prohibit your desired choice.