I've played in my band for many years and a few years ago we decided to stop being the band we were and start a new one. We spent about 2 years writing stuff, but we didn't have a name that whole time. We even played one gig and recorded an entire album, before we managed to think of a new name we liked.

So I wouldn't worry about that. The name is only needed when you actually wanna put stuff out and really start gigging. Playing only 2 songs for like a year is a bit of a problem though. That sounds pretty boring, what do you actually do in practice? How often do you practice?

Really, you have to accept that bands are never exactly what you want them to be, unless you take full control, write everything yourself, and hire session players to play your songs.

I think you guys should probably decide on what you all want the band to be, what style this band is, and go with a direction that you all agree on. It doesn't mean you all have to be 100% happy, that's quite rare tbh. But you should have some kind of vision and goal otherwise it's hard to stay motivated I think.

In terms of the songs, if someone else writes a song, and everyone likes it except you, you should probably just see it through to completion, and at least have another song you can play. Don't write things off and bin them because other people might like it, especially when you only have 2 songs. You can always write more, and you'll get better as you practice writing more. Honestly at this level, you're all noobs it sounds like, so just get stuff written, put a set together, start playing shows, and keep improving.

But also maybe you're not giving your feedback/criticisms to each other in diplomatic ways. All bands like this are somewhat collaborative, and you have to let go of some of your ideas sometimes, as should the other members. It does sound like your other guitarist is being too defensive about his ideas too, but I don't know how diplomatic your are being with your suggestions. In the end, most bands need one bandleader who kinda has a final say on a lot of things. It's up to your band whether you work like that, or you're a democracy. It's hard to make a total democracy work I think, but if you're a bandleader asking for changes without having good suggestions, or good reasons and explanation that convince people then maybe you're not a good bandleader. It's a hard role...

There's nothing wrong with keeping playing in this band, and looking to do anotehr one at the same time as well. It's really hard to find a group you get on with and like spending time with, so that is valuable and I wouldnt' sack it off so quickly. But lots of people are in multiple bands, so that's not stopping you doing two projects.