What's a more natural column name for Tables whose name share a column name?
Personally, I usually like my column names to be meaningful, as it makes it easier to follow in queries. I can see Scotts Hodgin's point, certainly, but you could end up with a query that looks like:

SELECT cust.full_name
      ,stat.name
      ,type.name
      ,clhd.name
      ,src.name
....


Of course, good table names or aliases can ameliorate my complaint (even in my example, you can take a stab at what these things might be). However, (again, for me) having to use 20 different columns with the same name in a query can make it easier to use the wrong one in the wrong place, and can make it harder to catch. I'd rather see:

SELECT cust.full_name
      ,stat.status
      ,type.cust_type
      ,clhd.reason
      ,src.source
....


Again - I'm presenting my perspective - this is really something that is a matter of personal taste.

It is a good idea to ask a team to be consistent. If you're the team lead, you can either dictate (your preference wins), take a vote (if most people want one option, then compliance with that option should be better), or ignore it (leading to the best chance of confusion for all).