There's a few different degrees of nickname names. Some, like Ella (for Isabella) and Liam (for William) have become legitimate names in their own right. Others are so far removed from their full forms that they're no longer even recognizable as nicknames: Molly for Mary or Jack for John. And then there are all those names in the middle ground -- names that many parents use, but are still closely linked with their full versions: Alex for Alexander, Kate for Katherine, and yes, Bastion for Sebastian.
There are also many different routes that parents go. Some select the nickname version of the name, wanting their kids to only be called by the pet version. Others choose the full name and are adamant that others only use that version. And there are those who choose a full name but use the nickname, with the assumption that their child will switch to the full version sometime in adulthood, when they want a more mature name.
What kind of namer are you? Does your child have a nickname? Do you mind? Did you choose the nickname?