照れ屋さん means "a shy person", but I don't understand why there's a さん. When I googled it I saw the usage of さん was nearly universal, but Google didn't say why.
What do you mean by "name is shy"? 照れ屋さん means "a shy person" as a whole.
屋 is a suffix with various meanings, one of which is "person who tends to do ～" or simply "-er". Examples:
- 照れ屋: a shy person
- 頑張り屋: a hard worker
- 寂しがり屋: someone who gets lonely easily; someone who cannot stand alone
- 気取り屋: a smug person
- 分からず屋: a stubborn/hardheaded person
This -さん has little to do with the meaning, but it is making the ～屋 word sound more friendly and/or prettier. Please see the links in the comment section. (It's not usually used with derogatory words like 気取り屋.)