The meaning of eudokia (εὐδοκία G2107), especially as used in Ephesians 1:5, is ambiguous (Ellicott’s commentary). The Expositor’s commentary provides a helpful summary of the occurrences of eudokia in the NT and some possible nuances of meaning.
Expositor’s Greek Testament
according to the good Pleasure of His will. Wycl. gives “by the
purpose of His will”; Rhem., “according to the purpose of His will”;
Tynd., “according to the pleasure of His will”; Cran., Gen., AV,
“according to the good pleasure of His will”. The noun εὐδοκία
(Vulg.-Clem., beneplacitum) is a biblical term. It is not current in
profane Greek, but represents the רָצוֹו of the OT (especially in the
Psalms), and occurs a good many times in Sir. In the NT it is found
thrice in the Gospels (Matthew 11:26; Luke 2:14; Luke 10:21), and six
times in the Pauline Epistles (Romans 10:1; Ephesians 1:5; Ephesians
1:9; Php 1:15; Php 2:13; 2 Thessalonians 1:11), but nowhere else. It
has the sense (a) of will (Matthew 11:26; Luke 10:21), passing into
that of desire (Romans 10:1); and (b) of good will (Luke 2:14;
Ephesians 1:9; Php 1:15; Php 2:13), passing into that of delight or
satisfaction (2 Thessalonians 1:11). Here it is taken by most (Mey.,
De Wette, Stier., Alf., Ell., Abbott, etc.) in the sense of
beneplacitum, purpose, sovereign counsel, as equivalent to κατὰ τὴν
βουλὴν τοῦ θελήματος αὐτοῦ in Ephesians 1:11.
As noted at the end of the above excerpt, there is a parallelism between verses 5 and 11, which helps to explain why translations such as the ESV have rendered two different Greek words, eudokia in v5 and prothesis in v11, as "purpose." The use of words that are far from synonymous does not support, however, an equivalency of meaning.
In context, Ephesians 1:5-12 details God’s purpose with respect to His will. While the word theléma (θέλημα G2307) is consistently used to reference God’s will, there are three different Greek nouns in Eph 1:5-12 that have “purpose” in their semantic range: eudokia, prothesis (πρόθεσις G4286 usage: a setting forth, the show-bread; purpose), and boulē (βουλή G1012 usage: counsel, decree).
To differentiate their use in Eph 1:5-12, it is helpful to consider the different connotations and uses of “purpose” as a verbal concept. Three aspects of purpose are particularly relevant to this discussion: 1) as referencing the reason behind something, with emphasis on the motive or intent 2) as referencing the reason/objective of something, with emphasis on the desired outcome 3) as referencing the function or instrumentality of something.
To illustrate, consider the different aspects of “purpose” in the giving of a gift. The giver wants to make someone happy - this is the purpose/motive behind the gift. The gift is given in order to make the receiver happy - this is the purpose/desired outcome of the gift. The gift is the means of making the receiver happy - this is the purpose/function of the gift.
Similarly, eudokia, prothesis, and boulē as used in Eph 1:5-12 relate to different aspects of God’s will. Following the above framework, eudokia is seen as referencing God's purpose/motive, prothesis the purpose/desired outcome, and boulē the purpose/counsel by which that outcome is achieved.
Ephesians 1:5-6 and 11-12 ESA [brackets added]
5 he predestined us for adoption to himself as sons
through Jesus Christ, according to the purpose [eudokia] of his
will, 6 to the praise of his glorious grace – Ephesians
1:5-6
11 In him we have obtained an inheritance, having been
predestined according to the purpose [prothesis] of him who works all
things according to the counsel [boulē] of his will, 12
so that we who were the first to hope in Christ might be to the praise
of his glory. – Ephesians 1:11-12
The noun eudokia is a presumed compound of eu (εὖ G2095 meaning good, well) and dokeó (δοκέω G1380 meaning to seem). Literally, it refers to that which seems good/pleasing. The eu in eudokia implies an underlying goodness/benevolence that can be sensed in every occurrence of the word.
Barnes commentary on Eph 1:5
The word rendered "good pleasure" - (εὐδοκία eudokia) - means "a
being well pleased;" delight in anything, favor, good-will, Luke 2:14;
Philippians 1:15; compare Luke 12:32. Then it denotes purpose, or
will, the idea of benevolence being included - Robinson.
While the parallelism between verses 5 and 11 does not mean they are equivalent, it does serve as a link between the two verses. I see the connection as indicative of a harmony between the intent, desired outcome, and counsel of God’s will. Of these, eudokia is seen as the basis from which everything else flows. Inherent to eudokia is the idea of goodness/benevolence that is, I believe, reflective of God’s nature. As such, eudokia inspires trust in God and His purpose for those who love Him (cf Rom 8:28, Jer 29:11, Ps 34:7-8).