It seems to me that I found the solution:
DECLARE @XML XML
DECLARE @ElementName VARCHAR(20)
SET @ElementName = 'city'
SELECT @XML = '
<employees>
<employee>
<name>Jacob</name>
<city>NY</city>
<team>SQL Server</team>
</employee>
<employee>
<name>Steve</name>
<city>NY</city>
<team>ASP.NET</team>
</employee>
</employees>'
--SET @XML.modify('delete (/employees/employee/*[local-name() = "city"])')
SET @XML.modify('delete (/employees/employee/*[local-name() = sql:variable("@ElementName")])')
SELECT @XML