My newborn keeps moving her neck to one side when she sleeps. Does that cause any issue with the baby's neck or head shape long term? I am currently putting a small flat pillow under her head for support and repositioning. Please advise.

It is not unusual for baby to favour one side when sleeping.
You could try changing her position in the cot/bassinet to be facing different way.
Red Nose does not recommend the use of a pillow in baby’s sleep environment.
https://rednose.org.au/article/pillow-use

Have you started tummy time when she is awake (& supervised)? This may help to reduce/prevent some altered head shape as well as build upper body strength.
Also, check with your GP or Child/Maternal Health Nurse to assess whether there is any potential tightening of a muscle in her neck. Infant Physiotherapist can also be helpful if needs be.