UK company established for .EU domains. Should be linked to oversea one?

[TECK]

Hi all,

We have an active limited company in UK, with all paperwork done and we are prepared for the .EU openings. No domains are registered yet through Sunrise.
We are also in the process to create a new corporation in Canada.
Do you recommend to get the same name like the UK one?
Legally, the canadian company could sell a domain that belongs to the UK company. You declare your taxes in Canada, not UK.

Thank you for your advice.