着 vs 著? Is it the same Is 着 the same as 著? Can I interchange them, for example:

Is

這位着名的歌手的名字是__


The same as

 這位著名的歌手的名字是__


(put a name in "__")
So here's a wrap up of the comments above.

着 is a Simplified Chinese only† character, so you won't find it in Traditional Chinese dictionaries, unless they explicitly list them. 

See e.g. 教育部重编国语辞典. (找不到, because there is not such character in Traditional Chinese) I assume that OP uses Traditional Chinese because of the 這 used in the example sentences.

† EDIT: *As @Stan pointed out above, 着 is used even outside of Mainland China, as a folk alternate form of 著, but it is not considered correct, at least in Taiwanese usage. However it is a proper form as 'zhe' in HK. 



However, we have 着 in Simplified Chinese where it corresponds mostly to the 著 character that is found both in Traditional and Simplified Chinese. The subtle, yet important difference is that when 著 is distinctively read 'zhù', it is written in both variants as 著 and in this case it doesn't correspond to 着. So 著名 is 著名 even in Simplified Chinese. In other cases - with different readings, like, 站著 (Trad.) corresponds to 站着 (Simpl.)

My theory is that some Simplified Chinese users are not aware of this use case and assume a 100% Simplified-Traditional correspondence between the two characters or even automatic ('character-by-character') machine transliteration could have contributed to the wrong assumption that 著名 can be written as 着名.