It depends on your paranoia level. Because of the way SSDs handle writing data, doing a zero-once on an SSD is not as good as doing so on a hard drive.
When you write a particular data page on an HD, the new data is simply written over the old data, replacing it. Write zeros over the whole disk and all the old data will be gone. SSDs, on the other hand, cannot simply overwrite individual pages. In order to replace the data on a page, the old data must first be erased, and SSDs cannot erase individual pages; they have to erase entire blocks consisting of many pages.
So what happens when you ask an SSD to overwrite, say, page #5, is that the SSD leaves the data on page #5 alone, but marks it as invalid, allocates another currently-blank page (say, #2305), writes the new data to page #2305, and makes a note that next time the OS asks for page #5 it should get #2305 instead. The original page #5 data sits there until some later time, when the drive needs more space, moves any remaining valid pages away from the block, and erases it. SSDs have more physical memory capacity than they expose to the computer, so they can juggle blocks like this for a while before actually having to erase anything (and when they do actually erase something, there's no good way to predict which blocks of leftover data will be chosen for erasure). See this AnandTech review for way more details (warning: it's fairly long, and the relevant stuff is spread around).
Net result: if you write zeros over the "whole" drive, you haven't actually overwritten all the old data. You have updated the controller's translation table so it'll never return any of the old data to the OS (those pages are all invalid). But if someone's hardcore enough to bypass the controller, they could get some of your data back.
Overwriting twice will probably work, but it depends on the controller's allocation strategy. Overwriting twice with random data (diskutil randomDisk 2 /dev/diskN) is a little more likely to work, but still not guaranteed. Both of these also have some bad side-effects: they uses some of the lifetime of the drive, and also increase the logical fragmentation on the SSD, decreasing its write performance.
Note that recent versions of OS X's graphical Disk Utility disable the secure erasure options on SSDs (for the reasons discussed above), but the command-line version still allows them. BTW, I have also seen several recommendations to securely erase SSDs by converting them to encrypted format, but this is (if anything) slightly less secure than overwriting with random data.
The best way to secure-erase an SSD is to invoke the controller's built-in secure-erase feature. This should (if the controller designers did their jobs) truly erase all blocks, and also have the side-effect of resetting the logical page map, essentially defragmenting it and restoring its original performance. Unfortunately, most of the utilities I've seen for doing this (e.g. CMRR's HDDErase) run under DOS, which won't boot on a Mac. I did find a posting on macrumors with (rather complex) instructions for doing a secure erase from a GParted boot CD. It might also be possible to use Parted Magic from a bootable flash drive, but I have not tried this.
Researchers at the Non-Volatile Systems Lab at UCSD have tested various ways of sanitizing SSDs by "erasing" the drive, then disassembling it to bypass the controller, and checking for remnant data (summary, full paper). Their results mostly agree with what I said above (and also show that the built-in secure-erase command isn't always implemented properly):
Our results lead to three conclusions:
First, built-in commands are effective, but manufacturers
sometimes implement them incorrectly. Second,
overwriting the entire visible address space of an SSD
twice is usually, but not always, sufficient to sanitize the
drive. Third, none of the existing hard drive-oriented
techniques for individual file sanitization are effective on
SSDs.
Your making a test user account with a short name different than the eventual user to be migrated is sound.
In practice, you will in time over write more and more of the data, but if you have the time to first establish a file vault key and have the drive completely encrypted before copying any sensitive data, you have a more secure system and can know that the data can be sanitized cryptographically as opposed to being over-written or actually erased.
You'll want to look for these lines in the diskutil cs list output to know it's ready for the start of data migration:
| Conversion Status: Complete
| High Level Queries: Fully Secure
| | Passphrase Required
Best Answer
You can't perform an erase because you have booted from the SSD. Hovering over the icon, will tell you why
To erase your SSD, boot from recovery or from a bootable USB then erase. If you are sending it for repair, just create another admin account and delete your user profile. It's much easier and just as secure. The moment you finish deleting your files, they will become unrecoverable