While they aren't exact equals, the synonymous poetry lines means "praise the name of the LORD" expresses the same idea as "blessed be the name of the LORD." In other words, praising the name of the LORD blesses the name of the LORD.
praise the name of the LORD!
Blessed be the name of the LORD
(Ps 113:1b–2a, ESV)
הַֽ֝לְלוּ אֶת־שֵׁ֥ם יְהוָֽה׃
יְהִ֤י שֵׁ֣ם יְהוָ֣ה מְבֹרָ֑ךְ
(Psalm 113:1b–2a, BHS2001)
"Blessed" translates a Pual particle. Note the following quote from HALOT.
pu: impf. יְבֹרַכְ/רָֽךְ; pt. מְבֹרָךְ, מְבֹרֶ֫כֶת, מְבֹרָכָיו (4QpPs 37 מבורכיו) —1. to be blessed Nu 22:6 2S 7:29 Ps 37:22 112:2 128:4 Pr 20:21 22:9 1C 17:27; מְבֹרֶכֶת י׳ blessed by Y. Dt 33:13, תְּבֹרַךְ מִן blessed among (or more than) Ju 5:24; —2. to be praised: God’s name Ps 113:2 Jb 1:21. †
Koehler, L., Baumgartner, W., Richardson, M. E. J., & Stamm, J. J. (1994–2000). In The Hebrew and Aramaic lexicon of the Old Testament (electronic ed., p. 160). E.J. Brill.
They were probably still saying the name YHWH when this was originally sung, which would have the meaning:
praise the name YHWH
Blessed be the name YHWH
Note: For the Jew the Name, hShem, is a way of referring to God without saying YHWH.
To praise the LORD is the task of all creation:
The heavens declare the glory of God,
and the sky above proclaims his handiwork.
2 Day to day pours out speech,
and night to night reveals knowledge.
3 There is no speech, nor are there words,
whose voice is not heard.
4 Their voice goes out through all the earth,
(Psalm 19:1–4, ESV)
Let everything that has breath praise the LORD!
Praise the LORD!
(Psalm 150:6, ESV)
Let all that breathes praise the LORD.
(Psalm 150:6, JPS1985)
כֹּ֣ל הַ֭נְּשָׁמָה תְּהַלֵּ֥ל יָ֗הּ הַֽלְלוּ־יָֽהּ
(Psalm 150:6, BHS2003)
is imperfect, which would tend to give it a future sense, except that it is jussive, which makes it like an imperative. Thus, the idea is that it should be continuous and not a single act.