OPtimum is going to push their router on you and not let you use FIOS routers. Both companies have the fact their routers make you a hotspot for them is not publicized very loudly. Optimum is not going to let you be a FIOS hotspot. Better off with your own router
FIOS customer equipment is NOT used to create hotspots, like Comcast's are. Unless you have some proof to the contrary. I'm a FIOS and a Comcast subscriber, and I can't say that I've EVER seen evidence of FIOS equipment setting up a public hotspot-type system, outside of what the user explicitly configures.
Methinks that you are un-informed.
Edit: And while I don't know much about Optimum or their equipment policies, my experience with various cable internet companies is, that you can either buy or rent a compatible modem to access their service, and then whatever router you chose to connect downstream, was up to you. (With the caveat that the cable ISP might supply a combo modem/router "gateway", that might have to be set to "bridge mode", to enable using your own router.)
Edit: OP, don't listen to QuietDad, he doesn't know what he's talking about, FIOS does not create public Hotspots with user equipment, either rented or owned. Not that I've ever seen, nor read about, and I'm a frequent visitor to some FIOS forums.
FIOS routers, CAN be re-purposed, and used just like a "regular" router, they have an ethernet WAN port (as well as a MOCA COAX WAN/LAN port). Assuming that you can just buy a compatible modem for Optimum, then you should be able to just plug in the FIOS router and go.
Edit: That said, unless you have the G1100 "Quantum Gateway" model, with the 802.11ac support, it's probably not even worth re-using the Verizon FIOS router that you have.
You would be better off in the long run, I feel, picking up an Asus router, AC66U, AC1750, AC66U B1, AC68U/R, AC1900, AC87U, AC88U, or newer, to run your network.
Or, depending on your wireless coverage needs, maybe a Google Wifi mesh setup, or an Asus AiMesh setup, or an Ubiquti EdgeRouter X and some AC-Pro APs, if you wanted to "get serious".
What speed will you have with your Optimum connection? (What rate plan?)