I purchased two small palm trees for gifts for the holidays. They did not have a name or care stick in them at the time of purchase. They are now not doing so well and I have no idea how to help as I don't know the name. The part that used to be green (leaves) has turned yellow from the inside to the outer edges. Someone informed me that it was the result of too much watering. However, the problem seems to have gotten worse since I have watered it less frequently. Help!!! Also, how would I find out the correct name?

Most indoor palms like and do very well in indirect bright light. If all you have is a sunny window, put them off to the side. Yellow leaves can be from over-watering or, they are in the wrong kind of light.
Water the palms well, then let the top inch or so dry before re-watering. The soil should feel slightly moist at all times. Watering them once a week should be fine, but if the soil feels wet after a week, wait another week. Go easy on the fertilizer, it should be diluted to half strength and given every few months from spring-early fall.