The basic definition of Hosanna is 'praise, adoration or joy' (I asked Siri!). Looking at Strong's via http://blueletterbible.org The word G5614 is used as an interjection; originally a cry for help, but later became an utterance of praise (Vine's). The origin is with two Hebrew roots (H3467) and (H4994).
I was seeing Ho-san-na in the English, but it is actually broken up more like Hosa-nna when related to the Hebrew roots. The transliteration of those words is yasha' (H3467) and na' (H4994).
Interestingly, Jehovah, Joshua, Yeshua (Hebrew) and the Greek equivalent Jesus are all related to the word group that includes yasha' (H3467). The concept is related with words all pertaining to salvation. Blue Letter Bible lists "to be open, wide, free, safe" or "causitively--to free, avenge, defend, deliver,...rescue, bring salvation, save(ior), get victory".
H4994 is a participle, na', that can mean "now, then, I pray". It is used for incitement or entreaty, such as "I beseech thee." (Ex. 33:18). It is translated "let" in Judges 13:8.
In Ps. 118:25, we also find yasha' translated as "Save now" and "I beseech thee" has a different Hebrew word--'anna' (H577)
I share all of this partly to answer my question, but also to broaden it a bit. Perhaps there is no linguistic connection, but is there rather a conceptual connection between Hosanna and Jehovah?
Only God saves in the spiritual sense, and often uses human agents to save in a physical sense, or with spiritual implications. Jesus, being both a human agent and God, was able to save and worthy of praise for being Savior and carried the name Yehoshua or Yeshua. These names identify Him with the Almighty, Holy One of Israel, YHWH.
Even if the people who cried, "Hosanna!" in Matthew 21:9, as either an entreaty, i.e. "Save us! Free us, now!" or as praise, i.e. "Deliverer! Victory!" did not make these conceptual connections, is there anything amiss about seeing such a relationship between Hosanna (Savior, save us!) and Jehovah, the God Who, because of His eternal existence, is able to save forever those who call upon His mercy?