I am purchasing a home without a mortgage. Are there any large problems which could arise if I put the title under my first initial and last name, vs. my full first name?

If would be best to you your legal name on the title to avoid any possible problems with the initial first. Just my opinion, not legal advise.

Yes - you need full names and identification in that name for the notary who witnesses your signature.

If you want to hold title in an LLC or separate LEGAL entity, quit claim the property to that entity later.