See Tractatus, 3.13: A proposition, therefore, does not actually contain its
sense, but does contain the possibility of expressing it. (‘The content of a proposition’ means the content of a proposition that has sense.)
A proposition contains the form, but not the content, of its sense.
Thus, propositions have sense (they express a content).
And see 3.203: A name means an object. The object is its meaning. Also 3.3: Only propositions have sense; only in the nexus of a proposition does a name have meaning.
It is reasonable that this point of view is derived from B.Russell; see PoM, §476: "Meaning and indication. The distinction between meaning (Sinn) and indication (Bedeutung) is roughly, though not exactly, equivalent to my distinction between a concept as such and what the concept denotes. [...] We must distinguish, [Frege] says, the meaning, in which is contained the way of being given, from what is indicated (from the Bedeutung). The indication of a proper name is the object
which it indicates; the presentation which goes with it is quite subjective; between the two lies the meaning, which is not subjective and yet is not the object. A proper name expresses its meaning, and indicates its indication. This theory of indication is more sweeping and general than mine, as appears from the fact that every proper name is supposed to have the two sides. It seems to me that only such proper names as are derived from concepts by means of the can be said to have meaning, and that such words as John merely indicate without meaning."
Regarding the "picture theory" and sense, see also What does bedeutung refer to in the Tractatus Logico-Philosophicus? as well as Making 'sense' of Wittgenstein's senselessness / nonsense distinction in the Tractatus and The Picture Theory of Meaning.