You can measure the battery to find what battery number it is. You can measure the space to see if a larger one will fit. A chart of battery dimensions is at: https://www.batteryweb.com/bci.cfm
. There is some variance between manufacturers, so your measurements may not be exact.
Typical RV batteries are BCI size 27. Yours could have been replaced with a different size, so see if a 27 will fit if yours is smaller.
And, yes, it should be a deep cycle battery, often sold as "RV and Marine". Avoid a Dual Rated Starting and Deep Cycle battery. They are not as good for RV coach service as a true deep cycle battery. If the battery lists CCA, cold cranking amps, pass on it.