Can I travel to the USA on the Visa Waiver Programme if........?

.....I have a conviction for obtaining goods by deception that is 10 years old, (no prison sentence) also a caution for affray that is 2 years old?
Also I should add that the first incident occured in my maiden name

Would not risk trying - you will be better off applying to the US embassy for a visa.

Probably not. Obtaining goods by deceptions indicates fraud which usually makes the offense a CIMT (crime involving moral turpitude). Is affray like disturbing the peace? If it is more like assault you should be ok unless you used a weapon or demonstrated a malicious intent.

Contact the embassy/consulate where you live. They should have up to date information about what offenses in your country come up to the level of a CIMT.

You should also go ahead and register with ESTA. You have to do that now to fly to the US and use the VWPP. If you aren't cleared by ESTA to use the VWPP you definitely will need a visa.

no, you cannot use the visa waiver.you must apply for a visa.
maiden name or not? it can be seen.your records follow you,
what is the caution for?
not sure about the latter one?

Depending upon how the statute is worded, it appears that you have been convicted of a crime involving moral turpitude. There's an excellent chance that you are not admissible pursuant to section 212(a)(2)(A)(i)(I) of the Act even though it happened 10 years ago (unless you were under 18 at the time).

A caution is not considered a conviction for U.S. immigration purposes, and an affray probably does not involve moral turpitude.

So, no matter what name you used at the time of the first arrest and conviction, the chances of you being inadmissible are very close to 100%. Would probably be considered a CIMT.

You need to apply for a waiver of the ground of inadmissibility, and if the application is granted, you can apply for a visa.