Tips for making an assassin character:
1. Dedication to what you are doing and loyalty to it (be it a person, ideal or object in the rare case of money) are what sets an assassin above other killers. This is why they are sometimes called fanatics, because they have committed themselves to what they are doing.
2. Do not tell everyone in a crowded bar (or other public place) that you are an assassin especially if the place tends to have PCs in it that are mostly honorable or good aligned. If you're looking for business go through an intermediate. Otherwise the chances of someone trying to stop or kill you increase.
3. Choose a suitable weapon and do not display it all the time for everyone to see. (If you are a child assassin - I really hate those btw. - do not choose a weapon that is inappropriate to your size, like 2 rapiers.) Change or discard weapons as necessary.
4. Vary the way you kill people or have a secret ID (like Zorro.)
5. Act professionally. An assassin is a professional killer. Not just a killer. Your average thug can kill. You are not a thug. Do not knowingly insult people.
6. Have good escape routes and cover your tracks. This is essential. If you are caught the likelihood of survival is very low unless you have people who are too nice to you (it is actually advisable that you kill yourself instead of divulging who you work for or your allies so your plans can continue after your death.)
7. Do your own homework. Do not trust everyone with the secrets you know. Learn who you deal with and why they do what they do. You may end up having to trust one or two with some of your secrets - but not everyone with somethings and not some people with everything.