A BOOL is a C scalar type, and NSNumber is an object. You can't use objects directly with the C ==, !=, <, >, etc. operators; you need the scalar values.
Also, YES and NO are the values typically used for BOOL, not TRUE and FALSE, though either should work really.
BOOL value = NO;
BOOL value2 = [name isEqualToString:[groupArray objectAtIndex:0]];
NSNumber *boolNumber = [NSNumber numberWithBool:YES];
NSNumber *boolNumber2 = [NSNumber numberWithBool:value2];
if (value2 == [boolNumber boolValue])
{
...
}
if (![boolNumber2 boolValue])
{
...
}
if (value)
{
...
}