Rather than listing achievements, it helps to start from what a Turing Machine actually is and reason forward to why it earns Turing this title.
A Turing Machine is a theoretical device consisting of an infinitely long tape divided into cells, a read-write head that can move along the tape, and a fixed table of rules that determines what the head writes and how it moves based on the current cell's symbol and the machine's current internal state.
What makes this construction significant is that Turing proved such a simple, mechanical set of rules operating on a tape could, in principle, carry out any calculation that could be described by a well-defined procedure, meaning it could compute anything a human following an algorithm could compute.
A stored-program electronic computer works on the same underlying principle: it holds a sequence of instructions and data in memory (playing the role of the tape), and a processor reads, interprets, and acts on that memory according to fixed rules (playing the role of the read-write head and rule table), stepping through the computation exactly as the abstract Turing Machine does.
Because every modern digital computer's ability to execute arbitrary programs traces directly back to this tape-and-rules model that Turing defined decades before any electronic computer existed, he is regarded as the person whose work made the modern computer possible.
Therefore, the correct answer is Alan Turing.