Without more information I'd use

/^(?!$)[a-z]*\.?[a-z]*$/i

The negative lookahead prevents empty matches.

See this demo at regex101

Here are some ways to do it:

1. Deal separately where the input has has one dot, with optional letters surrounding it, or no dot (but then having at least one letter):

   /^([a-z]*\.[a-z]*|[a-z]+)$/i

2. Just capture letters and dots like you did, but don't allow the input to have two dots, using a negative look ahead:

   /^(?!(.*\.){2})([a-z.]+)$/i

3. Capture optional letters then an optional point and then optional letters, but forbid an empty input with a negative look-ahead:

   /^(?!$)([a-z]*\.?[a-z]*)$/i

If in any case the dot should not be at the start or end and not match an empty string, you can start the match with 1 or more chars a-z and then optionally match a dot and again 1 or more chars a-z:

/^[a-z]+(?:\.[a-z]+)?$/i

Regex demo