yes just the name - is there a need to register it as a trademark ? If I take the .ie and .com domain.
There is no need to register a trademark in order to protect it as a domain name - the two systems are different. If you have a domain name, no one else can use that domain name, but that won't give it exactly the same protection as a trademark. As you use the domain name, you will build up goodwill in it and may increase the common law rights you have in it which, over time, will give you pseudo trademark rights.
So the question is not whether you
need to register the trademark, but whether you
want to. If your company name is the same as your trademark and your domain name (e.g. Tesco, tesco.ie) or if your company name is the same as your product, then, from a purely commercial point of view, it may be worth registering the trademark. But if your company name is "Financial Advice Limited" and your domain name is "tax.ie" then I wouldn't bother registering either of those as trademarks - because the value in the brand in that case is automatically made up of the domain name (tax.ie) and not the domain prefix ("tax" - unregisterable if you give tax advice). If the prefix of the domain name is what you consider to be valuable and it's not purely a web-based business, then that makes the case for registering the name as a trademark stronger. That's just my judgment though from a commercial standpoint.
The first portion of your original question (what class) is answered by hhhhhhhh. The second part of your original question can't be answered as stated - you can try to register any name you want as a trademark (you may not be successful depending on the name). Whether that name is part of a domain name is irrelevant. You need to decide whether you want to protect the brand via a domain name AND a trademark.
Sprite