Is there a name for someone who thinks he's got very good taste but in reality lacks it?

Solution 1:

Pseud is close to what you want. Merriam-Webster defines one as "a person who pretends to be an intellectual". It commonly refers to someone who pretends to have sophisticated artistic tastes but doesn't. There is a difference between having good taste and appearing an intellectual, but often part of being an intellectual is knowing what is considered good art, music, literature, fine dining, and other forms of culture.

Lexico has various examples with people who pretend to have sophisticated cultural tastes but are deluded or faking it. "I mean, you just know he watched all the New York pseuds sitting down for a performance of his entirely-silent composition 4'33, and had serious trouble keeping from giggling." "What began life as a joke at the expense of a junior TV researcher was to become one of the largest media deceptions in modern times, along the way pricking the pomposity of the many intellectual pseuds who descend on Edinburgh every August."

There are other terms like "nouveau riche" which mock people who are newly rich and spend their money in an over-the-top and tasteless way, but that's just a subset of those with no taste, and you can be tasteless without being nouveau riche.