Of course you want her to make friends:)

I also suggest you look into CAPD.

Some signs of CAPD include things like: kid hears well in a quiet environment; child is very uncomfortable with loud noises; child acts deaf in a noisier environment.

You said your DD had already had a hearing test; was this test with a specialist who can test for CAPD or just the regular hearing test?

A kid who tests at the local audiologist as having normal or great hearing may hear well with each individual ear in that sound-proofed booth. However, that typical test does not test (1) hearing with background noises and (2) how the brain puts the sounds together.

An intro to CAPD and a quick check-list can be found at: http://kidshealth.org/parent/medical/ears/central_auditory.html Keep in mind that some of the indicators can be masked by being PG.

A more technical description and an exploration of giftedness with CAPD can be found from the Eides at: http://www.neurolearning.com/auditory2.htm

The good news is that there is a lot you can do if a child does have CAPD, from ear filters to teaching your kid to stand right near the teacher in the loud room, to parents not freaking out that something else is wrong with the kid:) I know a number of PG kids with CAPD.

Not sure about the name recall: does this happen when she hears names in a louder environment or is fatigued from sound, or is this common in all environments?

About friends: I would try to isolate the real issue with making friends. If this is a hearing challenge, she might just be overwhelmed and have a hard time in nosier environments. How does she do in smaller group play? Is she more comfortable playing with just one other kid in a quiet environment?

I would also wonder about playing with peers (same age and ability). Has she had the opportunity to play with other PG kids?

You asked about a number of topics. I would think it would be helpful to figure out whether they may or may not be connected. Some may relate to an underlying issue (e.g. CAPD) and others may relate to other issues (introvert prefers to play with one friend, or child is more comfortable with peers).