Yes, name your boat, it's part of the fun of it all. Boat names are very much part of the yachting and sport-fishing culture.
Here's my thread on getting my boat name created on bus-graphic vinyl:
http://www.greatgrady.com/forum/viewtopic.php?t=4672
Dad got our first boat when I was about 5, they had 5 or 6 of them going from 22' to 42'. I bought my first boat when I was 19, a 22 footer, and I've owned 6 others up to 42'.
Here are the various boat names we've had:
Happy Ours
After Ours
After Ours Too
Solamar
Aurora
Mari-Mari
and finally...Chum-A-Long
There was a 15' Zodiak and a 8' pram in there that didn't have a name, and the wooden skiff I built never got the name board carved, but it was always "GULL". Dinghies don't always get a name, but it's common if they belong to a yacht.
Here's a link to Boldwater Graphics for some ideas of how some fellows get their fishing boat names applied, and there are some great boat names for sure:
http://www.boldwater.com
These folks had a lot of influence on how I developed my boat name and the graphics to go with it. They do charge a pretty penny for them, and either paint on or use the same graphic process I did.
I'm sure it's way too bold and 'in your face' for some of you, but we have a lot of fun with it and get tons of thumbs-up. When it's time to sell the buyer can decide if he wants it or not. If not, the vinyl is removable and then we'll buff out the hull. My boat doesn't get sunshine on the hull except when it's in the water. The rest of the time its on the trailer with a cover. I don't expect much fading to have to worry about it. The cut-out boot stripe is easily replaced.
One of the funnest things we do is cruise the harbors here in so-Cal and look at boats and boat names. I'm thinking you must feel your smaller Grady isn't good enough for a name, and that's just not true. Name her something that means something to you, and have a little fun with it!
BTW, my services are for hire, albiet it's definately a sideline for me 8)