Someone created a fake Facebook account with my name and altered a pic of me. Stalking me, what do I do?

[Eagle1 Fox2]

If you contact Facebook and let them know what is going on, they can and will remove his account and likely ban his real account too.

Also, even though he hasn't made any threats, what he is doing is harassment and is legally a crime. Take the Texas definition of harassment for example:

Sec. 42.07. HARASSMENT.
(a) A person commits an offense if, with intent to harass, annoy, alarm, abuse, torment, or embarrass another, he:

(7) sends repeated electronic communications in a manner reasonably likely to harass, annoy, alarm, abuse, torment, embarrass, or offend another.

In this case, the key words are harass and annoy. Odds are that the police will not do anything about it because it is a minor crime and often only a misdemeanor, but at least you would have something on record.