Just to make sure:
1. Portal (unnamed) on island > back to base-portal (unnamend)
2. New portal (unnamed) somewhere new > portal on island > was that one still unnamed?

I mean I might be dull atm and have trouble reading but i don't read that the only other unnamed portal was at your base (?).
If 1. portal at base > 2. portal island > 3. portal somewhere else and all have the same name (or are unnamed) i believe portal no. 3 will connect to no. 2. If you build a no. 4, it should then connect to no. 3 iirc.
So the problem is not, that you have more than 2 portals with the same name, right (which won't work)?
I mean if i'm absolutely wrong here, please let me know. But if anyone is using this kind of system, i personally wouldn't bet on it working 100% of times.