Okay, so before we set up the poll we need to agree on the rules based on the suggestions:
Timescale: one month
Number of votes: two per person
Series of polls using single transferrable vote, so that two names will battle it out for the final choice.
Based on this we set up a poll to run for an agreed timescale e.g. eliminate the name with the lowest number of votes each week. As we have only five suggestions this could influence the timescale. At the end of this initial voting period the count is carried to the next poll.
What do we do if we have several with the same amount of votes or zero votes?
I'd still favour a system where we have a series of polls with lowest scoring name dropping out each round until we are left with two names to battle it out in the final.
Single Transferrable Vote:
"an electoral system of proportional representation in which a person's vote can be transferred to a second or further competing candidate (according to the voter's stated order of preference) if the candidate of first choice is eliminated during a succession of counts or has more votes than are needed for election."