No, the WEBID is not used for logging purposes or SSH access, you are thinking of a user name, which is quite different from the WEBID. Note that you do have the option during the sign-up process of choosing the first user name under your account.
The current DreamHost preferred way of creating a referral link is by using your account number (eg: r.cgi?1234567), not your WEBID. In-fact, the rewards section of the panel no longer mentions the WEBID in the ‘How to refer people’ section. I’d say that the only reason that DreamHost has not disabled the r.cgi?WEBID referral links is that there are a lot of such referral links out there that they do not wish to suddenly make invalid.
It is perfectly logical, like I said DreamHost has decided to deprecate (or phase out) the use of WEBIDs.
I suspect you mean when registering a new account, because creating a new user does not involve the creation of a WEBID. As far as I know, there is no way to manually choose your WEBID when you create a new account.
Save [color=#CC0000]$50[/color] on DreamHost plans using [color=#CC0000]PRICESLASH[/color] promo code (Click for DreamHost promo code details)