Hi. My guess would be Acoelorrhaphe wrightii, The Everglades Falm palm.

The trunk is more like a Robellini than the trunk on the Everglades Fan. Also, I don't know the right terminology, but the "fan" in my picture is more round (the leaf points go in a circle), whereas the Everglades, they are more of a semi-circle.

Definitely a Chamaerops humilis. The petioles are a little longer than usual so my guess is that it is probably shade grown. It looks nice and healthy!
-Alex

You're right, Alex. It's growing in shade. So, if I grew this in my house, I could expect a similar look?

Do these show a lot of variation in the amount of suckering? One of mine is mass of multiples--constantly pupping. Others are virtually solitary. Also, if there is this variation, I would assume it has implications for hardiness in colder areas where they might be marginal--with the strongly suckering ones having the advantage, or not...?

If you grew it in your house you would probably get a pretty similar look. They dont do great as indoor plants year round so I would take it outside during the summer months (in your climate they are very hardy though and will have no problems surviving your winters).
Nj, I notice a lot of variation in suckering with these. Mine only has 1 sucker and it is mature (it bloomed last spring). Usually they have a lot of suckers by now. I think mine is going to stay mostly solitary with only a few suckers since the main trunk is growing straight and there are no signs of other suckers right now.
-Alex

Could I grow this indoors from Nov-April? In a south facing window? I tried a Sabal palmetto seedling but it died within months (I think because of lack of light) and it only made 2 leaves then started dying even though I was very watchful of it and always maintained a good watering schedule. Would this palm be a good candidate for growing indoors for 1/2 the year(Nov-April)? Or should I pass?

Go for it! No, they are easier, and usually faster than Sabals. They even have a lower heat requirement for growth. Meds are full sun but will deal well with your Winter situation.

Any ideas on what it could be? Thanks!!!