Determine If Duplicate with Value in Adjacent Cell Considered

I have a worksheet with data that looks like this:

Name Group
Johnson 1
Smith 0
McDonald 2
Long 3
Smith 2
Long 1
McDonald 0
Johnson 3

In an adjacent cell I'd like to be able to indicate which names are duplicated, but are not in group 0. The result may look something like this:

Name Group Duplicate
Johnson 1 Yes
Smith 0 No
McDonald 2 No
Long 3 Yes
Smith 2 No
Long 1 Yes
McDonald 0 No
Johnson 3 Yes

I would prefer not to use VBA code.

Any and all help in solving this task is greatly appreciated.
Thanks.

Perhaps this:

=IF(B2=0,"No",IF(SUMPRODUCT(($A$2:$A$10=A2)*($B$2:$B$10<>0))>1,"Yes","No"))

Martin,
The more I think about it, maybe your first suggestion was correct. Who knows? If there was more data to work with then it would be clearer e.g.

Johnson 1 Yes
Smith 0 Yes (Yes because 2 names Smith are not in group 0??)
McDonald 2 No
Long 3 Yes
Smith 2 Yes (Yes because 2 names Smith are not in group 0??)
Long 1 Yes
McDonald 0 No
Johnson 3 Yes
Smith 1 Yes

..in which case your first suggestion is correct (and advanced apologies)

or

Johnson 1 Yes
Smith 0 No (stays No because group 0??)
McDonald 2 No
Long 3 Yes
Smith 2 Yes (because 2 names Smith not in group 0??)
Long 1 Yes
McDonald 0 No
Johnson 3 Yes
Smith 1 Yes (because 2 names Smith not in group 0??)

or

Johnson 1 Yes
Smith 0 No (stays No because the name Smith is in group 0??)
McDonald 2 No
Long 3 Yes
Smith 2 No (stays No because the name Smith is in group 0??)
Long 1 Yes
McDonald 0 No
Johnson 3 Yes
Smith 1 No (stays No because the name Smith is in group 0??)

...HELP!!