Can a person be just a Christian and have private devotions at home alone and not assemble with other Christians for worship? NO!
All Christians are expected to assemble for worship with other Christians. This was the practice of the early church. For example Paul and Barnabas were obviously in the habit of assembly with the church in whatever city they found themselves. We have this record of their stay in Antioch: “And it came to pass, that a whole year they [Paul and Barnabas] assembled themselves with the church and taught much people.” (Acts 11:26) In the Book of Hebrews Christians are urged to assemble regularly: “Let us consider one another to provoke unto love and good works: not forsaking the assembling of ourselves together, as the manner of some is; but exhorting one another: and so much the more, as ye see the day approaching.” (Hebrews 10:25)
A person can certainly be just a Christian and not a part of any man-made denomination. Nevertheless, he or she is expected to assemble regularly for worship with others who are also just Christians. This is the way it was in the beginning. The North main Street Church of Christ is such an assembly of just Christians.