They might call it any of those, but stroller is the US term. If you were to call this a stroller in the UK it would be very unusual.
Your intended area may have its own preference, other names include:
- buggy
- pram
- push chair
Baby carriage would be understood but very old fashioned.
Which one to use?
Choose Stroller in the USA, and either pram or push chair elsewhere. Regionally people may disagree but you will discover this quickly and people will generally understand.