Characters that share exact names screw with quests in a few ways. This is what's been encountered so far:
The pair of them cannot take a quest together even if the minimum party size is 2. This was encountered trying to accept the magic manor quest in Ticker Square.
If more PCs are involved and a quest is accepted, only one of them is added. In our case, the person who spoke with the NPC and received the quest token did not receive the quest in their journal. This was encountered when accepting the frog quest in the Ponds.
If one of them accepted a quest the other could not be added afterwards using the quest token. This was encountered when attempting to add one of the PCs to the kobold quest in the Ponds.
It's possible that if one PC accepts and completes a quest then the other cannot take it. This possibly occurred when one PC couldn't take the cheese rat quest in Ticker Square after the other had finished it. I wasn't able to confirm this for the bug report as I was able to accept and finish a quest that the other character had also done. In that case it was the haunted opera that worked out fine.
I remember needing a DM to wand us in for a similar situation. Not sure there's a fix...