Most anchor lockers (well designed ones, anyways) will have some way to tie off the rode end. Typically, in smaller boats like yours, it'll be something like a u-bolt bolted in place along the bow keel - usually on the opposite side of the bow eye. But, yes, definitely tie it off solid. It's not to be used for holding the boat at anchor. It's so you don't accidentally lose your anchor if you happen to let all the rode out without paying attention.
When I was about 7 years old, I was with my grandfather, father and uncle. We were in a little 18' boat and were setting the anchor to do some fishing. They tossed the anchor and were talking as the rode was paying out. They were in the bow and I was behind them (it was a cramped little bow). I looked up at my grandpa and started to "Grandpa, the..." and he interrupted me saying "Wait a minute, I'm talking to your uncle". I said "But, grandpa..." Again, I got the "Just hold on a minute" response. So I stood there, with no way to get to the bow, and watched as the end of the rode wriggled out, like a frightened gardener snake slithering away from you in the grass, and over the bow disappearing into the water. A few seconds later, after the rode had completely vanished into the abyss, my grandfather (who still did not know the rode was gone) turned back to me and asked "What did you want to ask me". I pointed and simply, quietly said "the rope". His response? "Why didn't you tell me!" So, yes, I always make sure to have the end of the rode tied off, now!