In this question Yemon Choi asked whether there is a standard term for Banach algebras for which the submultiplicative law ($\|ab\| \leq \|a\| \|b\|$) is weakened to merely requiring the product to be continuous. When looking for an answer I discovered that Gelfand originally used the terms "normed ring" and "Banach algebra" in this weaker sense.

I'm working on a second edition of my book on Lipschitz algebras, and I still find that the "max" norm $\max(\|f\|_\infty, L(f))$ is the most appropriate one, despite failing to be submultiplicative.

It has been noted that the term "Banach algebra" is unfair to Gelfand, who is uncontroversially credited with developing their basic theory. How about using "Gelfand algebra" as a name for the above mentioned weakening of the (now standard) definition of Banach algebras? Are there other good options I'm not aware of?