I think going with Tim is a good idea. I'm actually in a similar position myself. I found that although most people seem to remember me because I have such an unusual firstname, they have a hard time pronouncing it. So I use my nickname (Zuly) instead of my firstname. Zuly is still uncommon, so people tend to remember me, yet it is easy to pronounce.
I use my firstname on all official business documents (bank accounts, contracts, etc), but use Zuly any other time (my blog, email, etc).
EDIT (to address your question about your lastname):
I don't think you'll have a problem if you choose to use a different last name from your legal one. In my case, I legally have two last names, but I only use one last name. I've been doing that for decades in the USA without a single problem. My legal name is Firstname Lastname1 Lastname2, but I’m known as Nickname Lastname1.
Another example is middle names...most people have middle names, but they rarely use them. If you search through all the blogs (or business cards) you'll be hard pressed to find a single person posting as Firstname Middlename Lastname. They want to be known as Firstname Lastname, just like I want to be known as Nickname Lastname, you want to be known as Tim Kara, and Georgios Kyriacos Panayiotou wants to be known as George Michael (stealing Fernando’s example). It's legal. All you’re trying to do is create a brand for yourself.
When most people are online they like to see informal names. Using Tim Kara will make you seem more friendly, real, and welcoming. And may help people relate to you better. Now when you have to sign a legal document you will sign using your legal name. I hope this helps, but if you still feel uncomfortable about it, speak to an attorney.