Not directly, but loosely, perhaps. Allusions are made when an earlier text contains an isolated, distinct motif that a later text wants to remind its audience of. This is not what is going on here, because gaining and losing one's “name” is a common idea in the biblical text.
In Hebrew, the word we translate “name” actually has a broader meaning. It often ...
In Philippians 4:5, what does Paul mean by "the Lord is at hand"?
That God is near to hear the prayers of his servants.
Philippians 4:5-6 NASB
5 Let your gentle spirit be known to all people. The Lord is [a]near.
6 Do not be anxious about anything, but in everything by prayer and
pleading with thanksgiving let your requests be made known to God.
These ideas are not mutually exclusive: “The Lord is at Hand” can mean both. It can mean that we are to act as if the return of the Lord is imminent per the OT prophecies quoted above. It can also mean that we are to act as if the Lord was near us in out daily walk with Him.