Was this character able to become one with the Force at the end of The Rise of Skywalker?

Yes, he was a Force Ghost. His body disappeared, in current canon this makes him a Force Ghost.

In an interview, Star Wars screenwriter Chris Terrio explained the rationale behind him not appearing alongside Luke and Leia, also insinuating that Ben Solo was a Force Ghost by accepting that he is an option to appear, so that supports what we already know.

What was the rationale behind only showing Luke and Leia’s Force Ghosts on Tatooine and not including the remaining Skywalkers, Anakin and Ben?

We absolutely discussed who would be there at the end. It’s not as though those Force ghosts will never appear to Rey now that she really is the first of the new Jedi. I think she has all of those Jedi behind her. J.J. was pretty clear about the idea that he didn’t want to take away from the moment of Leia finally appearing as a Force ghost and the twins finally being together.

[...]

It’s a fair question from fans because it’s a question that we debated endlessly — about what the final shot of Force ghosts would be. We spent hours and hours talking about this and debating it, and we decided that the moment when the Jedi have to be there for Rey, when it dramatically counts, is when she hears their voices. So, seeing them all at the end would be a lovely grace note, but we thought that Rey seeing her two masters, two Skywalkers, was stronger.
_{Hollywood Reporter}

The final sentence here being the short answer to your question:

we thought that Rey seeing her two masters, two Skywalkers, was stronger.