Hi Delphiarich! I see that you're working with your Droid X's mobile hotspot capability. Excellent! You can work with the security settings for your hotspot emitter by going into the 3G Mobile Hotspot menu, and then clicking on the Menu key (looks like 4 squares on the bottom left of your display) and then selecting Configure WiFi Hotspot.
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No it is not secure as I found out the hard way. Somehow my usage shows that I used 6 GB of data in 2 weeks! All I can figure is that someone tapped into my hotspot and was using it. It showed usage all hours of the day even around 3am when I was sleeping. Go into settings, wireless & networks, tethering & hotspot, mobile hotspot settings, configure mobile hotspot. I suggest changing the default password and uncheck the box that says "broadcast SSID". Also, you may want to manage allowed devices, device limit, and select the minimum amount which is 2 devices. This will improve performance and ensure that only the devices you authorize are accessing your hotspot. Some people are unaware that smartphones can get virus' and worms just like a computer. Hackers can potentially hack into your mobile hotspot. Keep an eye out for fluctuations in usage and usage at odd times of the day or night. (like when you know you were sleeping and not surfing the net) I just installed the Verizon Mobile Security app to do virus and malware scans. It also has a device locator in case your device goes missing. It will show your device on a map, you can sound an alarm if you misplace your phone, lock the phone, and erase the data from your device.